Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Guofeng Che and Haibo Chen

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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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1523412051

Digital Object Identifier
doi:10.36045/bbms/1523412051

Mathematical Reviews number (MathSciNet)
MR3784504

Zentralblatt MATH identifier
06882540

Subjects
Primary: 35B38: Critical points 35J35: Variational methods for higher-order elliptic equations 35J62: Quasilinear elliptic equations

Keywords
Quasilinear Schrödinger equation Variational methods Morse theory Local linking

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


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