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arXiv · 1804.00439

Periodic solutions to parameter-dependent equations with a $\phi$-Laplacian type operator

Guglielmo Feltrin·Elisa Sovrano·Fabio Zanolin
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Abstract

We study the periodic boundary value problem associated with the $\phi$-Laplacian equation of the form $(\phi(u'))'+f(u)u'+g(t,u)=s$, where $s$ is a real parameter, $f$ and $g$ are continuous functions, and $g$ is $T$-periodic in the variable $t$. The interest is in Ambrosetti-Prodi type alternatives which provide the existence of zero, one or two solutions depending on the choice of the parameter $s$. We investigate this problem for a broad family of nonlinearities, under non-uniform type conditions on $g(t,u)$ as $u\to \pm\infty$. We generalize, in a unified framework, various classical and recent results on parameter-dependent nonlinear equations.

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Guglielmo Feltrin, Elisa Sovrano, Fabio Zanolin. 2018-04-02. Periodic solutions to parameter-dependent equations with a $\phi$-Laplacian type operator. https://arxiv.org/abs/1804.00439

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