Coupled elliptic systems depending on the gradient with nonlocal BCs in exterior domains

TL;DR

This paper investigates the existence and multiplicity of positive radial solutions for a coupled elliptic system with gradient-dependent nonlinearities and nonlocal boundary conditions in exterior domains, using fixed point index theory.

Contribution

It introduces a novel approach with a non-standard cone to prove existence of solutions for complex elliptic systems with gradient dependence and nonlocal boundary conditions.

Findings

Established existence of positive radial solutions

Proved multiplicity results under certain conditions

Applied fixed point index theory in a new cone setting

Abstract

We study existence and multiplicity of positive radial solutions for a coupled elliptic system in exterior domains where the nonlinearities depend on the gradients and the boundary conditions are nonlocal. We use a non-standard cone to establish existence of solutions by means of fixed point index theory.