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Standing waves for 4-superlinear Schrödinger-Kirchhoff equations. (English) Zbl 1321.35018
Summary: We consider standing waves for 4-superlinear Schrödinger-Kirchhoff equations in \(\mathbb R^n\) with potential indefinite in sign. The nonlinearity considered in this study satisfies a condition that is much weaker than the classical Ambrosetti-Rabinowitz condition. We obtain a nontrivial solution and, in the case of odd nonlinearity, an unbounded sequence of solutions via the Morse theory and the Fountain theorem, respectively.

MSC:
35J20 Variational methods for second-order elliptic equations
35J60 Nonlinear elliptic equations
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