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arXiv · 2207.14583

Rich dynamics in planar systems with heterogeneous nonnegative weights

Julián López-Gómez·Eduardo Muñoz-Hernández·Fabio Zanolin
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Abstract

This paper studies the global structure of the set of nodal solutions of a generalized Sturm--Liouville boundary value problem associated to the quasilinear equation $$ -(\phi(u'))'= \lambda u + a(t)g(u), \quad \lambda\in {\mathbb R}, $$ where $a(t)$ is non-negative with some positive humps separated away by intervals of degeneracy where $a\equiv 0$. When $\phi(s)=s$ this equation includes a generalized prototype of a classical model going back to Moore and Nehari, 1959. This is the first paper where the general case when $\lambda\in\mathbb{R}$ has been addressed when $a\gneq 0$. The semilinear case with $a\lneq 0$ has been recently treated by L\'{o}pez-G\'{o}mez and Rabinowitz.

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Julián López-Gómez, Eduardo Muñoz-Hernández, Fabio Zanolin. 2022-07-29. Rich dynamics in planar systems with heterogeneous nonnegative weights. https://arxiv.org/abs/2207.14583

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