文摘
In this paper, we study the following biharmonic equations with mixed nonlinearity: \(\Delta^{2}u-\Delta u+V(x)u=f(x, u)+\lambda\xi(x)|u|^{p-2}u\) , \(x\in{ \mathbb {R}}^{N}\) , \(u\in H^{2}({\mathbb {R}}^{N})\) , where \(V\in C(\mathbb{R}^{N})\) , \(\xi\in L^{\frac{2}{2-p}}(\mathbb {R}^{N})\) , \(1\leq p , and \(\lambda>0\) is a parameter. The existence of multiple solutions is obtained via variational methods. Some recent results are improved and extended.