Multiple positive radial solutions for Neumann elliptic systems with gradient dependence

TL;DR

This paper investigates the existence, non-existence, and multiplicity of non-negative radial solutions for Neumann elliptic systems with gradient dependence on an annulus, using topological fixed point index methods.

Contribution

It introduces new topological results for elliptic systems with gradient dependence, expanding understanding of solution multiplicity under Neumann boundary conditions.

Findings

Established conditions for existence of solutions

Identified scenarios for non-existence

Provided examples illustrating the theory

Abstract

We provide new results on the existence, non-existence and multiplicity of non-negative radial solutions for semilinear elliptic systems with Neumann 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.