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arXiv · 1810.08397

Infinitely many solutions of a class of elliptic equations with variable exponent

Chang-Mu Chu·Haidong Liu
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Abstract

This paper is concerned with the $p(x)$-Laplacian equation of the form \begin{equation}\label{eq0.1} \left\{\begin{array}{ll} -\Delta_{p(x)} u=Q(x)|u|^{r(x)-2}u, &\mbox{in}\ \Omega,\\ u=0, &\mbox{on}\ \partial \Omega, \end{array}\right. \end{equation} where $\Omega\subset\R^N$ is a smooth bounded domain, $1 p^+$ and $Q: \overline{\Omega}\to\R$ is a nonnegative continuous function. We prove that \eqref{eq0.1} has infinitely many small solutions and infinitely many large solutions by using the Clark's theorem and the symmetric mountain pass lemma.

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Chang-Mu Chu, Haidong Liu. 2018-10-19. Infinitely many solutions of a class of elliptic equations with variable exponent. https://arxiv.org/abs/1810.08397

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