Abstract
We prove the existence of at least one $T$-periodic solution $(T> 0)$ for differential equations of the form $$ \left(\frac{u'(t)}{\sqrt{1-{u'}^2(t)}}\right)' =f(u(t))+h(t),\quad \text{in } (0,T), $$ where $f$ is a continuous function defined on $\mathbb{R}$ that satisfies a strong resonance condition, $h$ is continuous and with zero mean value. Our method uses variational techniques for nonsmooth functionals.
Citation
Laura Gonella. "Existence of periodic solutions for some singular elliptic equations with strong resonant data." Topol. Methods Nonlinear Anal. 43 (1) 157 - 170, 2014.
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