The weighted periodic-parabolic degenerate logistic equation

TL;DR

This paper characterizes the existence of positive periodic solutions for a broad class of weighted periodic-parabolic degenerate logistic equations, extending previous results and introducing new insights relevant to Population Dynamics.

Contribution

It generalizes existing theorems for degenerate logistic equations and enlarges the class of weights admitting positive solutions, with new implications for Population Dynamics.

Findings

Characterization of positive periodic solutions for degenerate logistic equations.

Extension of previous theorems to broader classes of weights.

Introduction of new results with no elliptic counterparts, relevant to Population Dynamics.

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.