Electron. J. Diff. Equ., Vol. 2015 (2015), No. 91, pp. 1-9.

Existence of solutions to quasilinear Schrodinger equations with indefinite potential

Zupei Shen, Zhiqing Han

Abstract:
In this article, we study the existence and multiplicity of solutions of the quasilinear Schrodinger equation
$$ -u''+V(x)u-(|u| ^2)''u=f(u) $$
on $\mathbb{R}$, where the potential $V$ allows sign changing and the nonlinearity satisfies conditions weaker than the classical Ambrosetti-Rabinowitz condition. By a local linking theorem and the fountain theorem, we obtain the existence and multiplicity of solutions for the equation.

Submitted October 24, 2014. Published April 10, 2015.
Math Subject Classifications: 37J45, 58E05, 34C37, 70H05.
Key Words: Quasilinear Schrodinger equation; local linking; fountain theorem; indefinite potential.

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Zupei Shen
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
email: pershen@mail.dlut.edu.cn
Zhiqing Han
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
email: hanzhiq@dlut.edu.cn Phone(Fax) +86 41184707268

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