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arXiv · 2110.14492

The weighted periodic-parabolic degenerate logistic equation

D. Aleja·I. Antón·J. López-Gómez
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Abstract

The main goal of this paper is twofold. First, it characterizes the existence of positive periodic solutions for a general class of weighted periodic-parabolic logistic problems of degenerate type (see (1.1)). This result provides us with is a substantial generalization of Theorem 1.1 of Daners and L\'opez-G\'omez [12] even for the elliptic counterpart of (1.1), and of some previous findings of the authors in [1] and [2]. Then, it sharpens some results of [19] by enlarging the class of critical degenerate weight functions for which (1.1) admits a positive periodic solution in an unbounded interval of values of the parameter $\lambda$. The latest findings, not having any previous elliptic counterpart, are utterly new and of great interest in Population Dynamics.

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D. Aleja, I. Antón, J. López-Gómez. 2021-10-27. The weighted periodic-parabolic degenerate logistic equation. https://arxiv.org/abs/2110.14492

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