Nonzero positive solutions of a multi-parameter elliptic system with functional BCs

TL;DR

This paper establishes new topological methods to prove the existence of nonzero positive weak solutions for multi-parameter elliptic systems with general functional boundary conditions, including non-existence results and illustrative examples.

Contribution

It introduces a general framework for multi-parameter elliptic systems with functional boundary conditions and proves existence and non-existence results using topological methods.

Findings

Existence of positive solutions under broad boundary conditions

Non-existence results for certain parameter ranges

Applicability demonstrated through examples

Abstract

We prove, by topological methods, new results on the existence of nonzero positive weak solutions for a class of multi-parameter second order elliptic systems subject to functional boundary conditions. The setting is fairly general and covers the case of multi-point, integral and nonlinear boundary conditions. We also present a non-existence result. We provide some examples to illustrate the applicability our theoretical results.