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 \(\frac{{f(x,u)}}{{\left| u \right|^{p - 2} u}} \to + \infty as u \to \infty \).
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Supported by the National Natural Science Foundation of China (10171032) and the Guangdong Provincial Natural Science Foundation (011606).
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Chen, Z., Shen, Y. Infinitely many solutions of dirichlet problem for p-mean curvature operator. Appl. Math. Chin. Univ. 18, 161–172 (2003). https://doi.org/10.1007/s11766-003-0020-7
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DOI: https://doi.org/10.1007/s11766-003-0020-7