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Electronic Journal of Differential Equations
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