Existence and multiplicity of weak solutions for nonuniformly elliptic equations with nonstandard growth condition

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dc.contributor.authorMashiyev, R. A.
dc.contributor.authorCekic, B.
dc.contributor.authorAvci, M.
dc.contributor.authorYucedag, Z.
dc.date.accessioned2024-04-24T17:07:52Z
dc.date.available2024-04-24T17:07:52Z
dc.date.issued2012
dc.departmentDicle Üniversitesien_US
dc.description.abstractWe discuss the problem - div(a(x, del u)) = m(x)vertical bar u vertical bar(r(x)-2) u + n(x)vertical bar u vertical bar(s(x)-2)u in Omega, where Omega is a bounded domain with smooth boundary in R-N(N >= 2), and div(a(x, del u)) is a p(x)-Laplace type operator with 1 < r(x)< p(x)< s(x). We show the existence of infinitely many nontrivial weak solutions in W-0(1,p(x))(Omega). Our approach relies on the theory of the variable exponent Lebesgue and Sobolev spaces combined with adequate variational methods and a variation of the Mountain Pass lemma and critical point theory.en_US
dc.description.sponsorshipDicle University, Turkey [DUBAP -10-FF-15]en_US
dc.description.sponsorshipThe authors thank the referees for their valuable suggestions and helpful corrections, which have improved the presentation of this article. This research project was supported by DUBAP -10-FF-15, Dicle University, Turkey.en_US
dc.identifier.doi10.1080/17476933.2011.598928
dc.identifier.endpage595en_US
dc.identifier.issn1747-6933
dc.identifier.issn1747-6941
dc.identifier.issue5en_US
dc.identifier.scopus2-s2.0-84859620326
dc.identifier.scopusqualityQ2
dc.identifier.startpage579en_US
dc.identifier.urihttps://doi.org/10.1080/17476933.2011.598928
dc.identifier.urihttps://hdl.handle.net/11468/17058
dc.identifier.volume57en_US
dc.identifier.wosWOS:000305021300008
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoenen_US
dc.publisherTaylor & Francis Ltden_US
dc.relation.ispartofComplex Variables and Elliptic Equations
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectP(X)-Laplace Operatoren_US
dc.subjectNonuniform Elliptic Equationsen_US
dc.subjectCritical Pointen_US
dc.subjectMultiple Solutionsen_US
dc.subjectEkeland's Variational Principleen_US
dc.subjectMountain Pass Theoremen_US
dc.titleExistence and multiplicity of weak solutions for nonuniformly elliptic equations with nonstandard growth conditionen_US
dc.titleExistence and multiplicity of weak solutions for nonuniformly elliptic equations with nonstandard growth condition
dc.typeArticleen_US

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