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- W2068351490 abstract "In this paper we study the following nonlinear boundary-value problem [-Delta_{p(x)} u=lambda f(x,u) quad text{ in } Omega,] [|nabla u|^{p(x)-2}frac{partial u}{partial nu}+beta(x)|u|^{p(x)-2}u=mu g(x,u) quad text{ on } partialOmega,] where (Omegasubsetmathbb{R}^N) is a bounded domain with smooth boundary (partialOmega), (frac{partial u}{partialnu}) is the outer unit normal derivative on (partialOmega), (lambda, mu) are two real numbers such that (lambda^{2}+mu^{2}neq0), (p) is a continuous function on (overline{Omega}) with (inf_{xin overline{Omega}} p(x)gt 1), (betain L^{infty}(partialOmega)) with (beta^{-}:=inf_{xin partialOmega}beta(x)gt 0) and (f : Omegatimesmathbb{R}rightarrow mathbb{R}), (g : partialOmegatimesmathbb{R}rightarrow mathbb{R}) are continuous functions. Under appropriate assumptions on (f) and (g), we obtain the existence and multiplicity of solutions using the variational method. The positive solution of the problem is also considered." @default.
- W2068351490 created "2016-06-24" @default.
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- W2068351490 date "2014-01-01" @default.
- W2068351490 modified "2023-09-25" @default.
- W2068351490 title "Existence and multiplicity results for nonlinear problems involving the p(x)-Laplace operator" @default.
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- W2068351490 doi "https://doi.org/10.7494/opmath.2014.34.3.621" @default.
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