Existence of solutions for $p(x)$-Laplacian problem on an unbounded domain
Keywords
Existence, p(x)-Laplacian problem, unbounded domainAbstract
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.Downloads
Published
2007-12-01
How to Cite
1.
YONGQIANG, Fu. Existence of solutions for $p(x)$-Laplacian problem on an unbounded domain. Topological Methods in Nonlinear Analysis. Online. 1 December 2007. Vol. 30, no. 2, pp. 235 - 250. [Accessed 28 March 2024].
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