Supersolutions to degenerated logistic equation type

TL;DR

This paper introduces a new method for constructing strictly positive supersolutions for degenerated logistic equations, aiding in understanding large solutions and applicable to boundary value problems with boundary-vanishing weights.

Contribution

The authors develop a straightforward approach to build supersolutions for degenerated logistic equations, advancing the analysis of boundary value problems with degenerated weights.

Findings

Method successfully constructs positive supersolutions.

Applicable to boundary value problems with boundary-vanishing weights.

Enhances understanding of large solutions in degenerated systems.

Abstract

In this work we provide a method for building up a strictly positive supersolution for the steady state of a degenerated logistic equation type, i.e., when the weight function vanishes on the boundary of the domain. This degenerated system is related in obtaining the so-called large solutions. Previously, this problem was handled as the limit case of non degenerated approaching problems. Our method can be adapted straightforwardly to degenerated boundary value problems.