Semi linear elliptic systems with dependence on the gradient

TL;DR

This paper investigates the existence, non-existence, and multiplicity of positive radial solutions for semi-linear elliptic systems with gradient dependence, using topological fixed point index methods.

Contribution

It introduces a topological approach to analyze semi-linear elliptic systems with gradient dependence, providing new existence and multiplicity results.

Findings

Established conditions for existence of solutions

Identified parameter ranges for non-existence

Illustrated theory with a concrete example

Abstract

We provide results on the existence, non-existence, multiplicity and localization of positive radial solutions for semi linear elliptic systems with Dirichlet or Robin boundary conditions on an annulus. Our approach is topological and relies on the classical fixed point index. We present an example to illustrate our theory.