On an elliptic Kirchhoff-type problem depending on two parameters

TL;DR

This paper investigates a Kirchhoff-type elliptic boundary value problem with two parameters, establishing conditions under which multiple solutions exist, thus contributing to the understanding of nonlinear elliptic equations with parameter dependence.

Contribution

The paper introduces new existence results for multiple solutions of a Kirchhoff-type problem depending on two parameters under general assumptions.

Findings

Existence of at least three solutions for certain parameter values.

Results hold under broad and natural conditions.

Provides insight into parameter-dependent nonlinear elliptic equations.

Abstract

In this paper, we consider the Dirichlet problem associated to an elliptic Kirchhoff-type equation depending on two parameters. Under rather general and natural assumptions, we prove that, for certain values of the parameters, the problem has at least three solutions.