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Bull. Korean Math. Soc. 2017; 54(3): 895-909

Online first article January 4, 2017      Printed May 31, 2017

https://doi.org/10.4134/BKMS.b160338

Copyright © The Korean Mathematical Society.

Infinitely many solutions for a class of modified nonlinear fourth-order elliptic equations on $\mathbb{R}^{N}$

Guofeng Che and Haibo Chen

Central South University, Central South University

Abstract

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This paper is concerned with the following fourth-order elliptic equations $$ \triangle^{2}u-\Delta u+V(x)u-\frac{\kappa}{2}\Delta(u^{2})u=f(x,u),\rm \mbox{ \ \ }in~\mathbb{R}^{N}, $$ where $N\leq6$, $\kappa\geq0$. Under some appropriate assumptions on $V(x)$ and $f(x, u)$, we prove the existence of infinitely many negative-energy solutions for the above system via the genus properties in critical point theory. Some recent results from the literature are extended.

Keywords: fourth-order elliptic equations, sublinear, nontrivial solutions, genus theory

MSC numbers: 35B38, 35J20

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