Work

Existence of Solutions for a Class of Kirchhoff-Type Equations with Indefinite Potential

Year: 2024

Type: article

Abstract: This study explores the existence of solutions to the following Kirchhoff-type problem\[\left\{\begin{array}[c]{ll}%-\left(a+b\int_{\mathbb{R}^3}|\nabla u|^2dx\right)\Delta u+ V(x)u=f(x,u),~{\rm{in}}~ \mathbb{R}^{3},\\u\in H^1(\mathbb{R}^3),%\end{array} %\right.\]where a and b are postive constants, and the potential \(V(x)\) is continuous and indefinite in sign. With suitable assumptions on \(V(x)\) and \(f\), we establish the existence of solutions using the Symmetric Mountain Pass Theorem.

Source: Electronic Journal of Applied Mathematics

DOI: 10.61383/ejam.20242368

Authors: Linlian Xiao, Jiaqian Yuan, Jian Zhou, Yunshun Wu

Institution: Guizhou Normal University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Guizhou Normal University, Department of Education of Guizhou Province

Awards: G4300404550, G6213351918