Existence and concentration of solutions for Schrödinger–Poisson system with steep potential well |
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| Authors: | Wen Zhang Xianhua Tang Jian Zhang |
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| Affiliation: | 1. School of Mathematics and Statistics, Central South University, Changsha, Hunan, China;2. School of Mathematics and Statistics, Hunan University of Commerce, Changsha, Hunan, China |
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| Abstract: | This paper is concerned with the nonlinear Schrödinger–Poisson system ![urn:x-wiley:mma:media:mma3712:mma3712-math-0001]( "urn:x-wiley:mma:media:mma3712:mma3712-math-0001") where λ > 0 is a parameter. We require that V≥0 and has a bounded potential well V?1(0). Combining this with other suitable assumptions on K and f, the existence of nontrivial solutions is obtained by using variational methods. Moreover, the concentration of solutions is also explored on the set V?1(0) as λ→∞. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | Schrö dinger– Poisson system sublinear variational methods concentration |
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