## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Existence of multiple nontrivial solutions for a class of quasilinear Schrödinger equations on $\mathbb{R}^{N}$

#### 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 and multiplicity of solutions for the above equations via variational methods. Recent results from the literature are extended.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 1 (2018), 39-53.

Dates
First available in Project Euclid: 11 April 2018

https://projecteuclid.org/euclid.bbms/1523412051

Digital Object Identifier
doi:10.36045/bbms/1523412051

Mathematical Reviews number (MathSciNet)
MR3784504

Zentralblatt MATH identifier
06882540

#### Citation

Che, Guofeng; Chen, Haibo. Existence of multiple nontrivial solutions for a class of quasilinear Schrödinger equations on $\mathbb{R}^{N}$. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 1, 39--53. doi:10.36045/bbms/1523412051. https://projecteuclid.org/euclid.bbms/1523412051