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- W1528163734 abstract "We study the existence and multiplicity results for the following nonlinear Neumann boundary-value problem involving the $p(x)$-Laplacian $$ (P_lambda)hspace{1cm} left{begin{array}{rllll}-operatorname{div} (|nabla u|^{p(x)-2}nabla u)+|u|^{p(x)-2}u & = & f(x,u)~~~mbox{ in }Omega, u & < & 0~~~~~~~~~~~mbox{ in }Omega, |nabla u|^{p(x)-2}frac{partial u}{partialnu} & = & lambda u^{q(x)}~~~~~mbox{ on }{partial}Omega , end{array} right. $$ where $Omegasubset mathbb R $ is a bounded domain with smooth boundary, $p(x)in C(barOmega),$ and $q(x)in C^{0,beta}({{partial}Omega})$ for some $betain(0,1)$. Under appropriate growth conditions on $f(x,u),$ $p(x),$ and $q(x)$ we show that there exists $Lambdain(0,infty)$ such that $(P_lambda)$ admits two solutions for $lambdain(0,Lambda)$, one solution for $lambda=Lambda$, and no solution for $lambda>Lambda$." @default.
- W1528163734 created "2016-06-24" @default.
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- W1528163734 date "2013-07-01" @default.
- W1528163734 modified "2023-10-18" @default.
- W1528163734 title "Global multiplicity results for $p(x)$-Laplacian equation with nonlinear Neumann boundary condition" @default.
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- W1528163734 doi "https://doi.org/10.57262/die/1369057818" @default.
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