Pairs of fixed points for a class of operators on Hilbert spaces

TL;DR

This paper establishes the existence of pairs of solutions for certain compact potential operators on Hilbert spaces and demonstrates an application to a second-order boundary value problem.

Contribution

It introduces new existence results for solution pairs of compact potential operators on Hilbert spaces, with an application to boundary value problems.

Findings

Existence of solution pairs for compact potential operators.

Application to second-order boundary value problems.

Provides a framework for analyzing solutions in Hilbert spaces.

Abstract

In this paper, existence of pairs of solutions is obtained for compact potential operators on Hilbert spaces. An application to a second-order boundary value problem is also given as an illustration of our results.