Existence of solutions for a nonhomogeneous Dirichlet problem

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dc.contributor.authorMarcos, Aboubacar
dc.contributor.authorAbdou, Aboubacar
dc.date.accessioned2022-04-20T12:01:20Z
dc.date.available2022-04-20T12:01:20Z
dc.date.issued2019
dc.description. A growing interest in the study of the p(x)- Laplacian operator has arisen during the last two decades, in regard to its involvement in the modelings of a large number of phenomena. One can name for instance electrorheological fluids [30, 32, 36], elastic mechanics, flows in porous media and image processing [11], curl systems emanating from electromagnetism [4, 7].en_US
dc.description.abstractWe obtain multiplicity and uniqueness results in the weak sense for the following nonhomogeneous quasilinear equation involving the p(x)-Laplacian operator with Dirichlet boundary condition: – p(x)u + V(x)|u| q(x)–2u = f(x, u) in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in RN, V is a given function with an indefinite sign in a suitable variable exponent Lebesgue space, f(x,t) is a Carathéodory function satisfying some growth conditions. Depending on the assumptions, the solutions set may consist of a bounded infinite sequence of solutions or a unique one. Our technique is based on a symmetric version of the mountain pass theorem.en_US
dc.description.sponsorshipWorld Banken_US
dc.identifier.citationMarcos, A., Abdou, A. (2019). Existence of solutions for a nonhomogeneous Dirichlet problem involving p(x)-Laplacian operator and indefinite weight. Springer Open Journal. Pg 1-21. https://doi.org/10.1186/s13661-019-1276-zen_US
dc.identifier.issnhttps://doi.org/10.1186/s13661-019-1276-z
dc.identifier.urihttp://hdl.handle.net/123456789/1403
dc.language.isoen_USen_US
dc.publisherSpringer Openen_US
dc.relation.ispartofseries;21
dc.subjectGeneralized Lebesgue–Sobolev spacesen_US
dc.subjectp(x)-Laplacian operatoren_US
dc.subjectSymmetric mountain pass lemmaen_US
dc.titleExistence of solutions for a nonhomogeneous Dirichlet problemen_US
dc.typeArticleen_US
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