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

TL;DR

This paper establishes the existence of at least one periodic solution for a class of singular elliptic differential equations with strong resonance, using variational methods for nonsmooth functionals.

Contribution

It introduces a novel application of variational techniques to prove solutions for singular elliptic equations under strong resonance conditions.

Findings

Proves existence of at least one T-periodic solution.

Utilizes variational methods for nonsmooth functionals.

Addresses equations with strong resonance conditions.

Abstract

We prove the existence of at least one T-periodic solution (T > 0) for differential equations of the form (u'(t)/sqrt{1-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.