Singular solutions of perturbed logistic-type equations

TL;DR

This paper analyzes positive singular solutions with boundary blow-up for perturbed logistic equations, establishing their exact blow-up rate and proving their uniqueness using Karamata regular variation theory.

Contribution

It introduces a precise characterization of blow-up rates and proves the uniqueness of singular solutions for a class of logistic-type equations with slow diffusion.

Findings

Exact blow-up rate determined near the boundary

Uniqueness of the singular solution established

Application of Karamata regular variation theory

Abstract

We are concerned with the qualitative analysis of positive singular solutions with blow-up boundary for a class of logistic-type equations with slow diffusion and variable potential. We establish the exact blow-up rate of solutions near the boundary in terms of Karamata regular variation theory. This enables us to deduce the uniqueness of the singular solution.