{"id":"https://openalex.org/W4412390936","doi":"https://doi.org/10.3390/axioms14070530","title":"Existence of Sign-Changing Solutions for a Class of p(x)-Biharmonic Kirchhoff-Type Equations","display_name":"Existence of Sign-Changing Solutions for a Class of p(x)-Biharmonic Kirchhoff-Type Equations","publication_year":2025,"publication_date":"2025-07-12","ids":{"openalex":"https://openalex.org/W4412390936","doi":"https://doi.org/10.3390/axioms14070530"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14070530","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070530","pdf_url":"https://www.mdpi.com/2075-1680/14/7/530/pdf?version=1752310927","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/7/530/pdf?version=1752310927","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5118975362","display_name":"Rui Deng","orcid":null},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Deng","raw_affiliation_strings":["School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China"],"raw_orcid":"https://orcid.org/0009-0003-0515-7453","affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China","institution_ids":["https://openalex.org/I145897649"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056141466","display_name":"Qing Miao","orcid":"https://orcid.org/0000-0001-8703-3603"},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qing Miao","raw_affiliation_strings":["School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China"],"raw_orcid":"https://orcid.org/0000-0001-8703-3603","affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China","institution_ids":["https://openalex.org/I145897649"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056141466"],"corresponding_institution_ids":["https://openalex.org/I145897649"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23712121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"7","first_page":"530","last_page":"530"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9991999864578247,"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":0.9991999864578247,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9958999752998352,"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/biharmonic-equation","display_name":"Biharmonic equation","score":0.9460242986679077},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.668226420879364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6380632519721985},{"id":"https://openalex.org/keywords/nehari-manifold","display_name":"Nehari manifold","score":0.5695236921310425},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5674458146095276},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.4836669862270355},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.47023481130599976},{"id":"https://openalex.org/keywords/p-laplacian","display_name":"p-Laplacian","score":0.44460999965667725},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.44070690870285034},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43567055463790894},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.425737202167511},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41426950693130493},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.4101523756980896},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29080379009246826},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.10562101006507874},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.09448519349098206},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08055359125137329}],"concepts":[{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.9460242986679077},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.668226420879364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6380632519721985},{"id":"https://openalex.org/C40332964","wikidata":"https://www.wikidata.org/wiki/Q6987780","display_name":"Nehari manifold","level":3,"score":0.5695236921310425},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5674458146095276},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.4836669862270355},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.47023481130599976},{"id":"https://openalex.org/C203269682","wikidata":"https://www.wikidata.org/wiki/Q7116898","display_name":"p-Laplacian","level":3,"score":0.44460999965667725},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.44070690870285034},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43567055463790894},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.425737202167511},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41426950693130493},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.4101523756980896},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29080379009246826},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.10562101006507874},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.09448519349098206},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08055359125137329},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14070530","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070530","pdf_url":"https://www.mdpi.com/2075-1680/14/7/530/pdf?version=1752310927","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:9a3ab472a4af4ee0abbacaad339a9391","is_oa":true,"landing_page_url":"https://doaj.org/article/9a3ab472a4af4ee0abbacaad339a9391","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,"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":"Axioms, Vol 14, Iss 7, p 530 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14070530","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070530","pdf_url":"https://www.mdpi.com/2075-1680/14/7/530/pdf?version=1752310927","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.7599999904632568}],"awards":[{"id":"https://openalex.org/G6958165847","display_name":"\u5177\u975e\u6807\u51c6\u589e\u957f\u6761\u4ef6\u7684p(x)-\u53cc\u8c03\u548c\u65b9\u7a0b\u89e3\u7684\u7814\u7a76","funder_award_id":"11861078","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412390936.pdf","grobid_xml":"https://content.openalex.org/works/W4412390936.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W67952865","https://openalex.org/W1481050868","https://openalex.org/W1599569396","https://openalex.org/W1627692906","https://openalex.org/W1965080837","https://openalex.org/W1966566141","https://openalex.org/W1973748816","https://openalex.org/W1986312993","https://openalex.org/W1996518052","https://openalex.org/W2007261596","https://openalex.org/W2018035406","https://openalex.org/W2019504076","https://openalex.org/W2023191117","https://openalex.org/W2034447457","https://openalex.org/W2038650644","https://openalex.org/W2056767073","https://openalex.org/W2065633914","https://openalex.org/W2070149682","https://openalex.org/W2077093149","https://openalex.org/W2079911808","https://openalex.org/W2081436513","https://openalex.org/W2088188233","https://openalex.org/W2109109248","https://openalex.org/W2398729868","https://openalex.org/W2748070915","https://openalex.org/W2793172287","https://openalex.org/W2809704317","https://openalex.org/W2886500774","https://openalex.org/W2906771323","https://openalex.org/W3036896263","https://openalex.org/W3086387797","https://openalex.org/W4232306901","https://openalex.org/W4404845600","https://openalex.org/W6628827349","https://openalex.org/W7011236903"],"related_works":["https://openalex.org/W3014882742","https://openalex.org/W4310275925","https://openalex.org/W4323313502","https://openalex.org/W4297734008","https://openalex.org/W2051917493","https://openalex.org/W2287651845","https://openalex.org/W2746516823","https://openalex.org/W2551995206","https://openalex.org/W2065449207","https://openalex.org/W4366169344"],"abstract_inverted_index":{"This":[0],"paper":[1],"mainly":[2],"studies":[3],"the":[4,10,21,39,46,68,77],"existence":[5],"of":[6,55,80],"sign-changing":[7,72],"solutions":[8],"for":[9],"following":[11],"px-biharmonic":[12],"Kirchhoff-type":[13],"equations:":[14],"\u2212a+b\u222bRN1p(x)|\u0394u|p(x)dx\u0394p(x)2u+V(x)|u|p(x)\u22122u":[15],"=":[16],"Kxf(u),x\u2208RN,":[17],"where":[18],"\u0394p(x)2u=\u0394|\u0394u|p(x)\u22122\u0394u":[19],"is":[20,58,84],"p(x)":[22],"biharmonic":[23],"operator,":[24],"a,b&gt;0":[25],"are":[26,30,62],"constants,":[27],"N\u22652,":[28],"V(x),K(x)":[29],"positive":[31],"continuous":[32],"functions":[33],"which":[34],"vanish":[35],"at":[36],"infinity,":[37],"and":[38,52],"nonlinearity":[40],"f":[41],"has":[42],"subcritical":[43],"growth.":[44],"Using":[45],"Nehari":[47],"manifold":[48],"method,":[49],"deformation":[50],"lemma,":[51],"other":[53],"techniques":[54],"analysis,":[56],"it":[57],"demonstrated":[59],"that":[60],"there":[61],"precisely":[63],"two":[64],"nodal":[65],"domains":[66],"in":[67],"problem\u2019s":[69],"least":[70],"energy":[71],"solution":[73],"ub.":[74],"In":[75],"addition,":[76],"convergence":[78],"property":[79],"ub":[81],"as":[82],"b\u21920":[83],"also":[85],"established.":[86]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
