{"id":"https://openalex.org/W3022461815","doi":"https://doi.org/10.1186/s13661-021-01545-2","title":"Nonlocal Lazer\u2013McKenna-type problem perturbed by the Hardy\u2019s potential and its parabolic equivalence","display_name":"Nonlocal Lazer\u2013McKenna-type problem perturbed by the Hardy\u2019s potential and its parabolic equivalence","publication_year":2021,"publication_date":"2021-07-31","ids":{"openalex":"https://openalex.org/W3022461815","doi":"https://doi.org/10.1186/s13661-021-01545-2","mag":"3022461815"},"language":"en","primary_location":{"id":"doi:10.1186/s13661-021-01545-2","doi":"https://doi.org/10.1186/s13661-021-01545-2","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13661-021-01545-2","pdf_url":"https://boundaryvalueproblems.springeropen.com/track/pdf/10.1186/s13661-021-01545-2","source":{"id":"https://openalex.org/S61795452","display_name":"Boundary Value Problems","issn_l":"1687-2762","issn":["1687-2762","1687-2770"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boundary Value Problems","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://boundaryvalueproblems.springeropen.com/track/pdf/10.1186/s13661-021-01545-2","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011786458","display_name":"Masoud Bayrami-Aminlouee","orcid":"https://orcid.org/0000-0002-4913-8890","observed_orcids":["https://orcid.org/0000-0002-4913-8890"]},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Masoud Bayrami-Aminlouee","raw_affiliation_strings":["Department of Mathematical Sciences, Sharif University of Technology, Azadi Ave, P.O. Box 11365-9415, Tehran, Iran","Sharif Univ. of Technology"],"raw_orcid":"https://orcid.org/0000-0002-4913-8890","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Sharif University of Technology, Azadi Ave, P.O. Box 11365-9415, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]},{"raw_affiliation_string":"Sharif Univ. of Technology","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007800091","display_name":"Mahmoud Hesaaraki","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mahmoud Hesaaraki","raw_affiliation_strings":["Department of Mathematical Sciences, Sharif University of Technology, Azadi Ave, P.O. Box 11365-9415, Tehran, Iran","Sharif Univ. of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Sharif University of Technology, Azadi Ave, P.O. Box 11365-9415, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]},{"raw_affiliation_string":"Sharif Univ. of Technology","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047720995","display_name":"Mohamed Karim Hamdani","orcid":"https://orcid.org/0000-0002-5597-2603","observed_orcids":["https://orcid.org/0000-0002-5597-2603","https://orcid.org/0000-0001-9242-4086"]},"institutions":[{"id":"https://openalex.org/I142899784","display_name":"University of Sfax","ror":"https://ror.org/04d4sd432","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784"]},{"id":"https://openalex.org/I4405252705","display_name":"Faculty of Sciences of Sfax","ror":"https://ror.org/01thp0k37","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784","https://openalex.org/I4405252705"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Mohamed Karim Hamdani","raw_affiliation_strings":["Mathematics Department, Faculty of Science of Sfax, University of Sfax, Sfax, Tunisia","Military Research Center, Science and Technology for Defense Laboratory LR19DN01, Aouina, Tunisia","Military School of Aeronautical Specialities, Sfax, Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science of Sfax, University of Sfax, Sfax, Tunisia","institution_ids":["https://openalex.org/I142899784","https://openalex.org/I4405252705"]},{"raw_affiliation_string":"Military Research Center, Science and Technology for Defense Laboratory LR19DN01, Aouina, Tunisia","institution_ids":[]},{"raw_affiliation_string":"Military School of Aeronautical Specialities, Sfax, Tunisia","institution_ids":["https://openalex.org/I142899784"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037610369","display_name":"Nguyen Thanh Chung","orcid":"https://orcid.org/0000-0001-7345-620X","observed_orcids":["https://orcid.org/0000-0001-7345-620X"]},"institutions":[{"id":"https://openalex.org/I4210136099","display_name":"Qu\u1ea3ng B\u00ecnh University","ror":"https://ror.org/045jvzr81","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210136099"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Nguyen Thanh Chung","raw_affiliation_strings":["Department of Mathematics, Quang Binh University, 312 Ly Thuong Kiet, Dong Hoi, Quang Binh, Vietnam","Department of Mathematics, Quang Binh University, Quang Binh, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quang Binh University, 312 Ly Thuong Kiet, Dong Hoi, Quang Binh, Vietnam","institution_ids":["https://openalex.org/I4210136099"]},{"raw_affiliation_string":"Department of Mathematics, Quang Binh University, Quang Binh, Vietnam","institution_ids":["https://openalex.org/I4210136099"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5011786458"],"corresponding_institution_ids":["https://openalex.org/I133529467"],"apc_list":{"value":1570,"currency":"USD","value_usd":1570},"apc_paid":{"value":1570,"currency":"USD","value_usd":1570},"fwci":0.21,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.32486915,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"2021","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-laplacian","display_name":"fractional Laplacian","score":0.9300000071525574},{"id":"https://openalex.org/keywords/hardy-potential","display_name":"Hardy potential","score":0.925000011920929},{"id":"https://openalex.org/keywords/singular-nonlinearity","display_name":"singular nonlinearity","score":0.9070000052452087},{"id":"https://openalex.org/keywords/positive-weak-solutions","display_name":"positive weak solutions","score":0.6940000057220459},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.7799999713897705},{"id":"https://openalex.org/keywords/blow-up","display_name":"blow-up","score":0.48100000619888306},{"id":"https://openalex.org/keywords/fractional-hardy-inequality","display_name":"fractional Hardy inequality","score":0.7799999713897705},{"id":"https://openalex.org/keywords/fractional-heat-equation","display_name":"fractional heat equation","score":0.3700000047683716},{"id":"https://openalex.org/keywords/bounded-smooth-domain","display_name":"bounded smooth domain","score":0.4390000104904175},{"id":"https://openalex.org/keywords/nonlocal-elliptic-problems","display_name":"nonlocal elliptic problems","score":0.5339999794960022},{"id":"https://openalex.org/keywords/nonexistence-of-solutions","display_name":"nonexistence of solutions","score":0.4480000138282776}],"concepts":[{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.7077203989028931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6707077026367188},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5928622484207153},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5113756060600281},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5102250576019287},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4505397379398346},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42440569400787354},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4232473373413086},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21304520964622498},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05664989352226257},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1186/s13661-021-01545-2","doi":"https://doi.org/10.1186/s13661-021-01545-2","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13661-021-01545-2","pdf_url":"https://boundaryvalueproblems.springeropen.com/track/pdf/10.1186/s13661-021-01545-2","source":{"id":"https://openalex.org/S61795452","display_name":"Boundary Value Problems","issn_l":"1687-2762","issn":["1687-2762","1687-2770"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boundary Value Problems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2005.05259","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.05259","pdf_url":"https://arxiv.org/pdf/2005.05259","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3022461815","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2005.05259","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:doaj.org/article:86a2869c1ee0413cb4ee044b88f500a2","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/86a2869c1ee0413cb4ee044b88f500a2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Boundary Value Problems, Vol 2021, Iss 1, Pp 1-42 (2021)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2005.05259","doi":"https://doi.org/10.48550/arxiv.2005.05259","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2005.05259","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1186/s13661-021-01545-2","doi":"https://doi.org/10.1186/s13661-021-01545-2","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13661-021-01545-2","pdf_url":"https://boundaryvalueproblems.springeropen.com/track/pdf/10.1186/s13661-021-01545-2","source":{"id":"https://openalex.org/S61795452","display_name":"Boundary Value Problems","issn_l":"1687-2762","issn":["1687-2762","1687-2770"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boundary Value Problems","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3022461815.pdf","grobid_xml":"https://content.openalex.org/works/W3022461815.grobid-xml"},"referenced_works_count":80,"referenced_works":["https://openalex.org/W285404633","https://openalex.org/W396478140","https://openalex.org/W1268530400","https://openalex.org/W1492085189","https://openalex.org/W1542891807","https://openalex.org/W1595395224","https://openalex.org/W1607530402","https://openalex.org/W1608238403","https://openalex.org/W1733365709","https://openalex.org/W1887438026","https://openalex.org/W1969983059","https://openalex.org/W1981151781","https://openalex.org/W1992201167","https://openalex.org/W1995655627","https://openalex.org/W1998699876","https://openalex.org/W2011095781","https://openalex.org/W2012495675","https://openalex.org/W2022231878","https://openalex.org/W2029009264","https://openalex.org/W2029386154","https://openalex.org/W2029473678","https://openalex.org/W2038280029","https://openalex.org/W2038991247","https://openalex.org/W2039707485","https://openalex.org/W2039745296","https://openalex.org/W2048982760","https://openalex.org/W2058405716","https://openalex.org/W2061118817","https://openalex.org/W2063001821","https://openalex.org/W2068042821","https://openalex.org/W2073078790","https://openalex.org/W2080588741","https://openalex.org/W2092194892","https://openalex.org/W2097415784","https://openalex.org/W2110780087","https://openalex.org/W2130440873","https://openalex.org/W2138239933","https://openalex.org/W2247508814","https://openalex.org/W2267305969","https://openalex.org/W2285636971","https://openalex.org/W2326641436","https://openalex.org/W2333138640","https://openalex.org/W2397969115","https://openalex.org/W2416490857","https://openalex.org/W2467327569","https://openalex.org/W2474098905","https://openalex.org/W2524560655","https://openalex.org/W2556073955","https://openalex.org/W2557439950","https://openalex.org/W2578165626","https://openalex.org/W2754693310","https://openalex.org/W2756421926","https://openalex.org/W2762041873","https://openalex.org/W2766598744","https://openalex.org/W2784649794","https://openalex.org/W2870489283","https://openalex.org/W2885560739","https://openalex.org/W2898936161","https://openalex.org/W2904147532","https://openalex.org/W2922503917","https://openalex.org/W2939292598","https://openalex.org/W2963227860","https://openalex.org/W2963470661","https://openalex.org/W2964090840","https://openalex.org/W2985563787","https://openalex.org/W2986530127","https://openalex.org/W3012641412","https://openalex.org/W3013285857","https://openalex.org/W3035838702","https://openalex.org/W3036627574","https://openalex.org/W3088001031","https://openalex.org/W3104655675","https://openalex.org/W3107270856","https://openalex.org/W3169811400","https://openalex.org/W4235853207","https://openalex.org/W4237950784","https://openalex.org/W4249274673","https://openalex.org/W4249642126","https://openalex.org/W4253117982","https://openalex.org/W4292081050"],"related_works":["https://openalex.org/W2807891456","https://openalex.org/W4206109660","https://openalex.org/W4399920880","https://openalex.org/W4280489686","https://openalex.org/W4289744367","https://openalex.org/W2610784520","https://openalex.org/W4391900873","https://openalex.org/W3030584787","https://openalex.org/W2058405716","https://openalex.org/W2922503917"],"abstract_inverted_index":{"Abstract":[0],"In":[1,305],"this":[2],"paper,":[3],"we":[4,141,173,189,208],"study":[5],"the":[6,12,19,133,137,149,157,162,182,199,210,214,218,306],"effect":[7],"of":[8,16,151,184,186,213],"Hardy":[9,139],"potential":[10],"on":[11],"existence":[13,150,176],"or":[14,312],"nonexistence":[15,192],"solutions":[17],"to":[18,156,161],"following":[20],"fractional":[21,138],"problem":[22,158,216],"involving":[23],"a":[24,100,143,152,166,191,194],"singular":[25],"nonlinearity:":[26],"$$\\begin{aligned}":[27,232],"\\textstyle\\begin{cases}":[28,233],"(-\\Delta":[29],")^{s}":[30,235],"u":[31,236,262],"=":[32,237],"\\lambda":[33,123,238],"\\frac{u}{":[34,239],"\\vert":[35,37,240,242],"x":[36,241],"^{2s}}":[38,243],"+":[39,244],"\\frac{\\mu":[40],"}{u^{\\gamma":[41],"}}+f":[42],"&":[43,49,55,247,255,264,275],"\\text{in":[44,50,56,248,256,265,276],"}":[45,51,57,249,257,266,277],"\\Omega,":[46,52],"\\\\":[47,53,253,261,273],"u>0":[48,68,254,285],"u=0":[54,71,288],"(\\mathbb{R}^{N}":[58,267],"\\setminus":[59,268],"\\Omega":[60,108,250,258,269],").":[61],"\\end{cases}\\displaystyle":[62,279],"\\end{aligned}$$":[63,280],"{":[64,281],"(\u2212\u0394)su=\u03bbu|x|2s+\u03bcu\u03b3+f":[65],"in":[66,69,72,136,217,283,286,289,292],"\u03a9,":[67,70],"(RN\u2216\u03a9).":[73],"Here":[74],"$0":[75,106,113],"<":[76],"s<1$":[77],"0<s<1":[78],",":[79,83,87,128,229],"$\\lambda":[80,201],">0$":[81,85],"\u03bb>0":[82],"$\\gamma":[84,313],"\u03b3>0":[86],"and":[88,145,177,180,193,224],"$\\Omega":[89],"\\subset":[90],"\\mathbb{R}^{N}$":[91],"\u03a9\u2282RN":[92],"(":[93],"$N":[94],">":[95,202],"2s$":[96],"N>2s":[97],")":[98,270],"is":[99],"bounded":[101],"smooth":[102],"domain":[103],"such":[104],"that":[105,230],"\\in":[107,116,296],"$":[109],"0\u2208\u03a9":[110],".":[111,120,206],"Moreover,":[112,188],"\\leq":[114,124,309],"\\mu,f":[115],"L^{1}(\\Omega":[117],")$":[118,298],"0\u2264\u03bc,f\u2208L1(\u03a9)":[119],"For":[121],"$0<":[122],"\\Lambda":[125,203],"_{N,s}$":[126,130,204],"0<\u03bb\u2264\u039bN,s":[127],"$\\Lambda":[129],"\u039bN,s":[131],"being":[132],"best":[134],"constant":[135],"inequality,":[140],"find":[142],"necessary":[144],"sufficient":[146],"condition":[147],"for":[148,165,198],"positive":[153],"weak":[154],"solution":[155],"with":[159,316],"respect":[160],"data\u03bcandf.":[163],"Also,":[164],"regular":[167],"datum":[168],"off,":[169],"under":[170],"suitable":[171,226],"assumptions,":[172],"obtain":[174],"some":[175,225],"uniqueness":[178],"results":[179],"calculate":[181],"rate":[183],"growth":[185],"solutions.":[187],"mention":[190],"complete":[195],"blowup":[196],"result":[197],"case":[200,219,307],"\u03bb>\u039bN,s":[205],"Besides,":[207],"consider":[209],"parabolic":[211],"equivalence":[212],"above":[215],"$\\mu":[220],"\\equiv":[221],"1$":[222,310],"\u03bc\u22611":[223],"$f(x,t)$":[227],"f(x,t)":[228],"is,":[231],"u_{t}+(-\\Delta":[234],"\\frac{1}{u^{\\gamma":[245],"}}+f(x,t)":[246],"\\times":[251,259,271],"(0,T),":[252,260,272],"=0":[263],"u(x,0)=u_{0}":[274],"\\mathbb{R}^{N},":[278],"ut+(\u2212\u0394)su=\u03bbu|x|2s+1u\u03b3+f(x,t)":[282],"\u03a9\u00d7(0,T),":[284,287],"(RN\u2216\u03a9)\u00d7(0,T),":[290],"u(x,0)=u0":[291],"RN,":[293],"where":[294],"$u_{0}":[295],"X_{0}^{s}(\\Omega":[297],"u0\u2208X0s(\u03a9)":[299],"satisfies":[300],"an":[301],"appropriate":[302],"cone":[303],"condition.":[304],"$0<\\gamma":[308],"0<\u03b3\u22641":[311],">1$":[314],"\u03b3>1":[315],"$2s(\\gamma":[317],"-1)<(\\gamma":[318],"+1)$":[319],"2s":[320]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2020-05-13T00:00:00"}