Multiple non-negative solutions of systems with coupled nonlinear BCs

TL;DR

This paper investigates the existence and multiplicity of non-negative solutions for boundary value problems with coupled nonlinear boundary conditions using fixed point index theory, providing a general framework and illustrative example.

Contribution

It introduces a general fixed point index approach to analyze coupled nonlinear boundary conditions, broadening the scope of solvable boundary value problems.

Findings

Established conditions for existence of solutions

Proved multiplicity results for solutions

Demonstrated the theory with a specific example

Abstract

Using the theory of fixed point index, we discuss the existence and multiplicity of non-negative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a variety of situations. We illustrate our theory in an example all the constants that occur in our theory.