INFINITELY MANY SOLUTIONS FOR FOURTH-ORDER ELLIPTIC EQUATIONS WITH SIGN-CHANGING POTENTIAL
INFINITELY MANY SOLUTIONS FOR FOURTH-ORDER ELLIPTIC EQUATIONS WITH SIGN-CHANGING POTENTIAL
复制标题
DOI：
10.11650/tjm.18.2014.3584
复制
发表时间：
2014-03
影响因子：
0.4
通讯作者：
Wen Zhang;Xianhua Tang;Jian Zhang
中科院分区：
文献类型：
--
作者：
Wen Zhang;Xianhua Tang;Jian Zhang
In this paper, we study the following fourth-order elliptic equation $$ \left\{ \begin{array}{ll} \Delta^{2}u-\Delta u+V(x)u=f(x, u), \ \ \ x\in\mathbb{R}^{N},\\ u\in H^{2}(\mathbb{R}^{N}), \end{array} \right. $$ where the potential $V\in C(\mathbb{R}^N, \mathbb{R})$ is allowed to be sign-changing. Under the weakest superquadratic conditions, we establish the existence of infinitely many solutions via variational methods for the above equation. Recent results from the literature are extended.
In this paper, we study the following fourth-order elliptic equation $$ \left\{ \begin{array}{ll} \Delta^{2}u-\Delta u+V(x)u=f(x, u), \ \ \ x\in\mathbb{R}^{N},\\ u\in H^{2}(\mathbb{R}^{N}), \end{array} \right. $$ where the potential $V\in C(\mathbb{R}^N, \mathbb{R})$ is allowed to be sign-changing. Under the weakest superquadratic conditions, we establish the existence of infinitely many solutions via variational methods for the above equation. Recent results from the literature are extended.