{"id":"https://openalex.org/W3206826628","doi":"https://doi.org/10.3934/mfc.2021023","title":"Bound state solutions for fractional Schr\u00f6dinger-Poisson systems","display_name":"Bound state solutions for fractional Schr\u00f6dinger-Poisson systems","publication_year":2021,"publication_date":"2021-10-20","ids":{"openalex":"https://openalex.org/W3206826628","doi":"https://doi.org/10.3934/mfc.2021023","mag":"3206826628"},"language":"en","primary_location":{"id":"doi:10.3934/mfc.2021023","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2021023","pdf_url":null,"source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/mfc.2021023","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103002828","display_name":"Xinsheng Du","orcid":"https://orcid.org/0000-0002-7458-0568"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xinsheng Du","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100350141","display_name":"Qi Li","orcid":"https://orcid.org/0000-0001-6422-5020"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qi Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073755802","display_name":"Zengqin Zhao","orcid":"https://orcid.org/0000-0001-8528-1785"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zengqin Zhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017776050","display_name":"Gen Li","orcid":"https://orcid.org/0000-0002-0288-9216"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gen Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9783,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.73670805,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"5","issue":"1","first_page":"57","last_page":"57"},"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":0.9965000152587891,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/combinatorics","display_name":"Combinatorics","score":0.5693840980529785},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49904322624206543}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5693840980529785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49904322624206543}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/mfc.2021023","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2021023","pdf_url":null,"source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/mfc.2021023","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2021023","pdf_url":null,"source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1484024929","https://openalex.org/W1511883840","https://openalex.org/W1536447298","https://openalex.org/W1973352373","https://openalex.org/W1981288703","https://openalex.org/W1986428751","https://openalex.org/W1990966857","https://openalex.org/W1992051250","https://openalex.org/W2007638845","https://openalex.org/W2008344080","https://openalex.org/W2011095781","https://openalex.org/W2022671370","https://openalex.org/W2049434583","https://openalex.org/W2050926333","https://openalex.org/W2058655685","https://openalex.org/W2065977294","https://openalex.org/W2070020532","https://openalex.org/W2086574007","https://openalex.org/W2123584176","https://openalex.org/W2130440873","https://openalex.org/W2172034033","https://openalex.org/W2327218125","https://openalex.org/W2527175614","https://openalex.org/W2570915431","https://openalex.org/W2603154707","https://openalex.org/W2756977120","https://openalex.org/W2789500280","https://openalex.org/W2792908645","https://openalex.org/W3021196877","https://openalex.org/W3101658996","https://openalex.org/W3103160692","https://openalex.org/W3103229763","https://openalex.org/W3124607094","https://openalex.org/W4232306901"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>In":[1],"this":[2],"work,":[3],"we":[4,64],"investigate":[5],"a":[6,57,89],"class":[7],"of":[8,106],"fractional":[9,84],"Schr\u00f6dinger":[10,85],"-":[11],"Poisson":[12],"systems</p><p":[13],"style='text-indent:20px;'><disp-formula>":[14],"<label/>":[15],"<tex-math":[16],"id=\"FE1\">":[17],"\\begin{document}$":[18],"\\begin{equation*}":[19],"\\left\\{\\begin{array}{ll}(-\\triangle)^s":[20],"u":[21,23],"+V(x)u+\\lambda\\phi":[22],"=":[24,32],"\\mu":[25],"u+|u|^{p-1}u,":[26],"&":[27,34],"x\\in\\":[28,35],"\\mathbb{R}^3,":[29,36],"\\\\(-\\triangle)^s":[30],"\\phi":[31],"u^2,":[33],"\\end{array}\\right.":[37],"\\end{equation*}":[38],"$\\end{document}":[39],"</tex-math></disp-formula></p><p":[40],"style='text-indent:20px;'>where":[41],"<inline-formula><tex-math":[42,47,52,69,77,98,107],"id=\"M1\">\\begin{document}$":[43],"s\\in(\\frac{3}{4},":[44],"1)":[45],"$\\end{document}</tex-math></inline-formula>,":[46,51,81],"id=\"M2\">\\begin{document}$":[48],"p\\in(3,":[49],"5)":[50],"id=\"M3\">\\begin{document}$":[53],"\\lambda":[54],"$\\end{document}</tex-math></inline-formula>":[55,72,101],"is":[56,102],"positive":[58,95],"parameter.":[59],"By":[60],"the":[61,82,103],"variational":[62],"method,":[63],"show":[65],"that":[66,74],"there":[67],"exists":[68],"id=\"M4\">\\begin{document}$":[70],"\\delta(\\lambda)>0":[71],"such":[73],"for":[75],"all":[76],"id=\"M5\">\\begin{document}$":[78],"\\mu\\in[\\mu_1,":[79],"\\mu_1+\\delta(\\lambda))":[80],"above":[83],"-Poisson":[86],"systems":[87],"possess":[88],"nonnegative":[90],"bound":[91],"state":[92],"solutions":[93],"with":[94],"energy.":[96],"Here":[97],"id=\"M6\">\\begin{document}$":[99],"\\mu_1":[100],"first":[104],"eigenvalue":[105],"id=\"M7\">\\begin{document}$":[108],"(-\\triangle)^s":[109],"+V(x)":[110],"$\\end{document}</tex-math></inline-formula>.</p>":[111]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}