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 Infinitely many solutions for a class of modified nonlinear fourth-order elliptic equations on $\mathbb{R}^{N}$ Bull. Korean Math. Soc. 2017 Vol. 54, No. 3, 895-909 https://doi.org/10.4134/BKMS.b160338Published online May 31, 2017 Guofeng Che and Haibo Chen Central South University, Central South University Abstract : 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 Downloads: Full-text PDF