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march 2018 Existence of multiple nontrivial solutions for a class of quasilinear Schrödinger equations on $\mathbb{R}^{N}$
Guofeng Che, Haibo Chen
Bull. Belg. Math. Soc. Simon Stevin 25(1): 39-53 (march 2018). DOI: 10.36045/bbms/1523412051

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.

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Guofeng Che. Haibo Chen. "Existence of multiple nontrivial solutions for a class of quasilinear Schrödinger equations on $\mathbb{R}^{N}$." Bull. Belg. Math. Soc. Simon Stevin 25 (1) 39 - 53, march 2018. https://doi.org/10.36045/bbms/1523412051

Information

Published: march 2018
First available in Project Euclid: 11 April 2018

zbMATH: 06882540
MathSciNet: MR3784504
Digital Object Identifier: 10.36045/bbms/1523412051

Subjects:
Primary: 35B38, 35J35, 35J62

Rights: Copyright © 2018 The Belgian Mathematical Society

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Vol.25 • No. 1 • march 2018
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