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arXiv · 1910.12014

Another multiplicity result for the periodic solutions of certain systems

Biagio Ricceri
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Abstract

In this paper, we deal with a problem of the type $$\cases{(\phi(u'))'=\nabla_xF(t,u) & in $[0,T]$\cr & \cr u(0)=u(T)\ , \hskip 3pt u'(0)=u'(T)\ ,\cr}$$ where, in particular, $\phi$ is a homeomorphism from an open ball of ${\bf R}^n$ onto ${\bf R}^n$. Using the theory developed by Brezis and Mawhin in [1] jointly with our minimax theorem proved in [3], we obtain a general multiplicity result, under assumptions of qualitative nature only. Three remarkable corollaries are also presented.

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Biagio Ricceri. 2019-10-26. Another multiplicity result for the periodic solutions of certain systems. https://arxiv.org/abs/1910.12014

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