On the structure of positive solutions for a class of quasilinear equations

TL;DR

This paper investigates the existence, uniqueness, and behavior of positive solutions for a class of quasilinear equations, using bifurcation, sub and supersolution methods, and large solution constructions.

Contribution

It provides new insights into the structure of positive solutions for quasilinear equations, including conditions for existence and uniqueness, and analyzes parameter effects.

Findings

Established conditions for existence and nonexistence of solutions

Proved uniqueness of positive solutions under certain conditions

Analyzed how solutions vary with parameters  and 

Abstract

This paper studies the existence, nonexistence and uniqueness of positive solutions for a class of quasilinear equations. We also analyze the behavior of this solutions with respect to two parameters $\kappa$ and $\lambda$ that appears in the equation. The proof of our main results relies on bifurcation techniques, the sub and supersolution method and a construction of an appropriate large solutions.