Existence of positive solution for a singular elliptic problem with an asymptotically linear nonlinearity

TL;DR

This paper investigates positive solutions for a singular elliptic problem with an asymptotically linear nonlinearity, employing variational and comparison methods to establish existence, uniqueness, non-existence, regularity, and bifurcation results.

Contribution

It introduces a comprehensive analysis combining variational and comparison techniques for singular elliptic problems with asymptotically linear nonlinearities, including bifurcation phenomena.

Findings

Existence of positive solutions under certain conditions

Uniqueness and non-existence results established

Bifurcation behavior identified

Abstract

In this paper we consider the existence of positive solutions for a singular elliptic problem involving an asymtotically linear nonlinearity and depending on one positive parameter. Using variational methods, together with comparison techniques, we show the existence, uniqueness, non-existence and regularity of the solutions. We also obtain a bifurcation-type result.