Existence of solutions to quasilinear Schrodinger equations with indefinite potential

• Main Authors: Zupei Shen, Zhiqing Han
• Format: Article
• Language: English
• Published: Texas State University 2015-04-01
• Series: Electronic Journal of Differential Equations
• Subjects: Quasilinear Schrodinger equation; local linking; fountain theorem; indefinite potential
• Online Access: http://ejde.math.txstate.edu/Volumes/2015/91/abstr.html

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.