Three solutions for a new Kirchhoff-type problem

TL;DR

This paper investigates the existence of multiple solutions for a new Kirchhoff-type problem with negative modulus, employing variational methods and critical point theory to establish the presence of three solutions under certain conditions.

Contribution

It introduces three solutions for a Kirchhoff-type problem with negative modulus using advanced variational techniques, which is a novel application in this context.

Findings

Existence of three nontrivial solutions for small parameters.

Application of Mountain Pass Lemma, Ekeland variational principle, and Minimax principle.

Solutions are proven via variational and algebraic analysis.

Abstract

This article concerns on the existence of multiple solutions for a new Kirchhoff-type problem with negative modulus. We prove that there exist three nontrivial solutions when the parameter is enough small via the variational methods and algebraic analysis. Moreover, our fundamental technique is one of the Mountain Pass Lemma, Ekeland variational principle, and Minimax principle.