Existence and Multiplicity of Solutions for a Biharmonic Kirchhoff Equation in $\mathbb{R}^5$

We consider the biharmonic equation $\Delta^2u-\left(a+b\int_{\R^5}|\nabla u|^2dx\right)\Delta u\\+V(x)u=f(u)$, 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 $p\in(2,10)$, where it was assumed $p\in(4,10)$ in many papers.