Year: 2024
Author: Ziqing Yuan, Sheng Liu
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 71–87
Abstract
We consider the biharmonic equation $∆^2u− (a+b\int_{\mathbb{R}^5} |∇u|^2 dx) ∆u + V (x)u = f(u),$ where $V(x)$ and $f(u)$ are continuous functions. By using a perturbation approach and the symmetric mountain pass theorem, the existence and multiplicity of solutions for this equation are obtained, and the power-type case $f(u) = |u|^ {p−2}u$ is extended to $p ∈ (2, 10),$ where it was assumed $p ∈ (4, 10)$ in many papers.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.71
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 71–87
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Biharmonic equation multiplicity of solutions variational method.