Infinitely many solutions for semilinear Schrödinger equations with sign-changing potential and nonlinearity

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Abstract

In this paper, we study the existence of infinitely many nontrivial solutions for a class of semilinear Schrödinger equations {-△u+V(x)u=f(x,u),x∈RN,u∈H1(RN), where the potential V is allowed to be sign-changing, and the primitive of the nonlinearity f is of super-quadratic growth near infinity in u and is also allowed to be sign-changing. Our super-quadratic growth conditions weaken the Ambrosetti-Rabinowitz type condition. © 2012 Elsevier Ltd.

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Tang, X. H. (2013). Infinitely many solutions for semilinear Schrödinger equations with sign-changing potential and nonlinearity. Journal of Mathematical Analysis and Applications, 401(1), 407–415. https://doi.org/10.1016/j.jmaa.2012.12.035

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