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arXiv · 1707.02532

On mountain pass theorem and its application to periodic solutions of some nonlinear discrete systems

Liang Ding·Jinlong Wei·Shiqing Zhang
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Abstract

We obtain a new quantitative deformation lemma, and then gain a new mountain pass theorem. More precisely, the new mountain pass theorem is independent of the functional value on the boundary of the mountain, which improves the well known results (\cite{AR,PS1,PS2,Qi,Wil}). Moreover, by our new mountain pass theorem, new existence of nontrivial periodic solutions for some nonlinear second-order discrete systems is obtained, which greatly improves the result in \cite{Z04}.

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Liang Ding, Jinlong Wei, Shiqing Zhang. 2017-07-09. On mountain pass theorem and its application to periodic solutions of some nonlinear discrete systems. https://arxiv.org/abs/1707.02532

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