Che, Guofeng; Chen, Haibo Existence of multiple nontrivial solutions for a class of quasilinear Schrödinger equations on \(\mathbb{R}^N\). (English) Zbl 1394.35191 Bull. Belg. Math. Soc. - Simon Stevin 25, No. 1, 39-53 (2018). Summary: This paper is concerned with the following fourth-order elliptic equations \[ \triangle^2 u- \Delta u + V(x)u - \frac{\kappa}{2}\Delta(u^2)u=f(x,u),\quad \text{in } \mathbb{R}^N, \] where \(N\leq6\), \(\kappa\geq0\). Under some appropriate assumptions on \(V(x)\) and \(f(x, u)\), we prove the existence and multiplicity of solutions for the above equations via variational methods. Recent results from the literature are extended. Cited in 5 Documents MSC: 35J62 Quasilinear elliptic equations 35J35 Variational methods for higher-order elliptic equations Keywords:fourth-order elliptic equation; multiplicity of solutions; variational methods PDFBibTeX XMLCite \textit{G. Che} and \textit{H. Chen}, Bull. Belg. Math. Soc. - Simon Stevin 25, No. 1, 39--53 (2018; Zbl 1394.35191) Full Text: Euclid