Existence of Periodic Solutions for some Singular Elliptic Equations with Strong Resonant Data

2011/12/14 by Laura Gonella, Gonella, Laura
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1112.3267

arxiv created 2011/12/14 · arxiv updated 2011/12/15

Abstract

We prove the existence of at least one T-periodic solution (T > 0) for differential equations of the form (u'(t)/sqrt1-u'²(t))'=f(u(t))+h(t), in (0,T), where f is a continuous function defined on R that satisfies a strong resonance condition, h is continuous and with zero mean value. Our method uses variational techniques for nonsmooth functionals.

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