Nontrivial solutions of boundary value problems for second order functional differential equations

TL;DR

This paper develops a general fixed point index approach on affine cones to establish the existence of multiple nontrivial solutions for a class of nonlocal boundary value problems involving second order functional differential equations.

Contribution

It introduces a novel fixed point index method on affine cones for solving nonlocal boundary value problems, expanding beyond traditional cone-based approaches.

Findings

Established conditions for multiple solutions

Applied the theory to specific functional differential equations

Provided illustrative examples of the solutions

Abstract

In this paper we present a theory for the existence of multiple nontrivial solutions for a class of perturbed Hammerstein integral equations. Our methodology, rather than to work directly in cones, is to utilize the theory of fixed point index on affine cones. This approach is fairly general and covers a class of nonlocal boundary value problems for functional differential equations. Some examples are given in order to illustrate our theoretical results.