Taiwanese Journal of Mathematics

INFINITELY MANY SOLUTIONS FOR FOURTH-ORDER ELLIPTIC EQUATIONS WITH SIGN-CHANGING POTENTIAL

Wen Zhang, Xianhua Tang, and Jian Zhang

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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.

Article information

Source
Taiwanese J. Math., Volume 18, Number 2 (2014), 645-659.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706406

Digital Object Identifier
doi:10.11650/tjm.18.2014.3584

Mathematical Reviews number (MathSciNet)
MR3188523

Zentralblatt MATH identifier
1357.35164

Subjects
Primary: 35J35: Variational methods for higher-order elliptic equations 35J60: Nonlinear elliptic equations

Keywords
fourth-order equations sign-changing potential superquadratic variational methods

Citation

Zhang, Wen; Tang, Xianhua; Zhang, Jian. INFINITELY MANY SOLUTIONS FOR FOURTH-ORDER ELLIPTIC EQUATIONS WITH SIGN-CHANGING POTENTIAL. Taiwanese J. Math. 18 (2014), no. 2, 645--659. doi:10.11650/tjm.18.2014.3584. https://projecteuclid.org/euclid.twjm/1499706406


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