Standing waves for 4‐superlinear Schrödinger‐Kirchhoff equations |
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| Authors: | Shaowei Chen Shibo Liu |
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| Institution: | 1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China |
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| Abstract: | We consider standing waves for 4‐superlinear Schrödinger–Kirchhoff equations in  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. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | Schrö dinger– Kirchhoff equations Palais– Smale condition Morse theory fountain theorem |
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