Nonzero radial solutions for a class of elliptic systems with nonlocal BCs on annular domains

TL;DR

This paper establishes new topological criteria for the existence and multiplicity of nonzero radial solutions in elliptic systems with nonlocal boundary conditions, using fixed point index methods and spectral radius comparisons.

Contribution

It introduces novel existence and multiplicity results for elliptic systems with nonlocal BCs, employing spectral radius comparisons and fixed point index techniques.

Findings

Multiple nonzero radial solutions are proven to exist.

Criteria for existence and non-existence are established.

An illustrative example demonstrates the theory's application.

Abstract

We provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of Hammerstein integral equations. Some of the criteria involve a comparison with the spectral radii of some associated linear operators. We apply our results to prove the existence of multiple nonzero radial solutions for some systems of elliptic boundary value problems subject to nonlocal boundary conditions. Our approach is topological and relies on the classical fixed point index. We present an example to illustrate our theory.