Three Solutions to a Neumann Problem for Elliptic Equations with Variable Exponent

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dc.contributor.authorMashiyev, R. A.
dc.date.accessioned2024-04-24T16:10:36Z
dc.date.available2024-04-24T16:10:36Z
dc.date.issued2011
dc.departmentDicle Üniversitesien_US
dc.description.abstractIn this article, we study the following nonlinear Neumann boundary value problem {(partial derivative u/partial derivative v) (-div(vertical bar del u vertical bar p(x)-2 del u) + a(x)vertical bar u vertical bar p(x)-2u = lambda f(x, u)) (on x is an element of partial derivative Omega) (in x is an element of Omega) where Omega subset of R-N (N >= 3), Omega is a bounded smooth domain and, p is an element of C ((Omega) over bar) with inf(x is an element of(Omega) over bar) p(x) > N, f : R -> R is a continuous function, and nu is the unit normal exterior vector on partial derivative Omega and a is an element of L-8(Omega), with ess infa(x) = a(0) > 0 and lambda > 0 is a real number. We first deal with the case that f (t) = b vertical bar t vertical bar(q-2)t - d vertical bar t vertical bar(s-2)t, t is an element of R, where b and d are positive constants. Then we deal with the case that f (x, t) = vertical bar t vertical bar(q(x)-2)t - vertical bar t vertical bar(s(x)-2)t, x is an element of Omega, t is an element of R, where q, s is an element of C ((Omega) over bar). Using the direct Ricceri variational principle, we establish the existence of at least three weak solutions of this problem in weighted-variable-exponent Sobolev space W-a(1,p(x)) (Omega).en_US
dc.identifier.doi10.1007/s13369-011-0141-x
dc.identifier.endpage1567en_US
dc.identifier.issn2193-567X
dc.identifier.issn2191-4281
dc.identifier.issue8en_US
dc.identifier.scopus2-s2.0-83755195877
dc.identifier.scopusqualityQ1
dc.identifier.startpage1559en_US
dc.identifier.urihttps://doi.org/10.1007/s13369-011-0141-x
dc.identifier.urihttps://hdl.handle.net/11468/14944
dc.identifier.volume36en_US
dc.identifier.wosWOS:000298294200008
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoenen_US
dc.publisherSpringer Heidelbergen_US
dc.relation.ispartofArabian Journal For Science and Engineering
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectP(X)-Laplacianen_US
dc.subjectVariable Exponent Lebesgue And Sobolev Spacesen_US
dc.subjectRicceri Variational Principleen_US
dc.titleThree Solutions to a Neumann Problem for Elliptic Equations with Variable Exponenten_US
dc.titleThree Solutions to a Neumann Problem for Elliptic Equations with Variable Exponent
dc.typeArticleen_US

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