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arXiv · 1709.05677

The Ambrosetti-Prodi periodic problem: Different routes to complex dynamics

Elisa Sovrano·Fabio Zanolin
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Abstract

We consider a second order nonlinear ordinary differential equation of the form $u'' + f(u) = p(t)$ where the forcing term $p(t)$ is a $T$-periodic function and the nonlinearity $f(u)$ satisfies the properties of Ambrosetti-Prodi problems. We discuss the existence of infinitely many periodic solutions as well as the presence of complex dynamics under different conditions on $p(t)$ and by using different kinds of approaches. On the one hand, we exploit the Melnikov's method and, on the other hand, the concept of "topological horseshoe".

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Elisa Sovrano, Fabio Zanolin. 2017-09-17. The Ambrosetti-Prodi periodic problem: Different routes to complex dynamics. https://arxiv.org/abs/1709.05677

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