Abstract
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.
Citation
Wen Zhang. Xianhua Tang. Jian Zhang. "INFINITELY MANY SOLUTIONS FOR FOURTH-ORDER ELLIPTIC EQUATIONS WITH SIGN-CHANGING POTENTIAL." Taiwanese J. Math. 18 (2) 645 - 659, 2014. https://doi.org/10.11650/tjm.18.2014.3584
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