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Infinitely many solutions of dirichlet problem for <Emphasis Type="Italic">p</Emphasis>-mean curvature operator

Authors:	Chen Zhihui Shen Yaotian

Institution:	(1) Dept. of Appl. Math., South China Univ. of Tech., 510640 Guangzhou, China

Abstract:	The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator: $\left\{ \begin{gathered} div((1 + \left\| {\nabla u} \right\|^2 )^{\frac{{P - 2}}{2}} \nabla u) = f(x,u), x \in \Omega , \hfill \\ u \in W_0^{1P} (\Omega ), \hfill \\ \end{gathered} \right.$ is considered, where Θ is a bounded domain in R ⁿ(n>p>1) with smooth boundary ∂Θ. Under some natural conditions together with some conditions weaker than (AR) condition, we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if $\frac{{f(x,u)}}{{\left\| u \right\|^{p - 2} u}} \to + \infty as u \to \infty$ . Supported by the National Natural Science Foundation of China (10171032) and the Guangdong Provincial Natural Science Foundation (011606).

Keywords:	35J60 35J35
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