TY - JOUR
T1 - Existence and Multiplicity of Solutions for a Biharmonic Kirchhoff Equation in $\mathbb{R}^5$
AU - Yuan , Ziqing
AU - Liu , Sheng
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 71
EP - 87
PY - 2024
DA - 2024/03
SN - 6
DO - http://doi.org/10.12150/jnma.2024.71
UR - https://global-sci.org/intro/article_detail/jnma/22967.html
KW - Biharmonic equation, multiplicity of solutions, variational method.
AB - <p style="text-align: justify;">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.</p>