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 Volume 10, Number 5, 2020, Pages 2024-2035 Infinitely many low- and high-energy solutions for a class of elliptic equations with variable exponent Chang-Mu Chu,Haidong Liu Keywords:$p(x)$-Laplacian, variable exponent, infinitely many solutions, Clark''s theorem, symmetric mountain pass lemma. Abstract: This paper is concerned with the $p(x)$-Laplacian equation of the form $$\left\{\begin{array}{ll} -\Delta_{p(x)} u=Q(x)|u|^{r(x)-2}u, &\mbox{in}\ \Omega,\u=0, &\mbox{on}\ \partial \Omega, \end{array}\right. \eqno{0.1}$$ where $\Omega\subset\R^N$ is a smooth bounded domain, $1p^+$ and $Q: \overline{\Omega}\to\R$ is a nonnegative continuous function. We prove that (0.1) has infinitely many small solutions and infinitely many large solutions by using the Clark''s theorem and the symmetric mountain pass lemma. PDF      Download reader