Existence of solutions for $p(x)$-Laplacian problem on an unbounded domain
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Existence, p(x)-Laplacian problem, unbounded domainAbstrakt
In this paper we study the following $p(x)$-Laplacian problem: $$ \alignat 2 -\div(a(x)|\nabla u|^{p(x)-2}\nabla u)+b(x)|u|^{p(x)-2}u&=f(x,u) &\quad& x\in \Omega,\\ u&=0 &\quad&\text{on }\partial\Omega, \endalignat $$ where $1< p_{1}\le p(x)\le p_{2}< n$, $\Omega\subset {\mathbb R}^{n}$ is an exterior domain. Applying Mountain Pass Theorem we obtain the existence of solutions in $W_{0}^{1,p(x)}(\Omega)$ for the $p(x)$-Laplacian problem in the superlinear case.Pobrania
Opublikowane
2007-12-01
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1.
YONGQIANG, Fu. Existence of solutions for $p(x)$-Laplacian problem on an unbounded domain. Topological Methods in Nonlinear Analysis [online]. 1 grudzień 2007, T. 30, nr 2, s. 235–250. [udostępniono 22.7.2024].
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