EXISTENCE OF SOLUTIONS TO QUASILINEAR SCHR¨ODINGERSCHR¨ SCHR¨ODINGER EQUATIONS WITH INDEFINITE POTENTIAL

Zupei Shen, Zhiqing Han
2015 Electronic Journal of Differential Equations   unpublished
In this article, we study the existence and multiplicity of solutions of the quasilinear Schrödinger equation −u + V (x)u − (|u| 2) u = f (u) on 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.
fatcat:bmnfvigdvfdyfdzawnaybsntwm