Ground state solutions for asymptotically periodic fractional Schrödinger–Poisson problems with asymptotically cubic or super‐cubic nonlinearities |
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Authors: | Sitong Chen Jiawu Peng Xianhua Tang |
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Institution: | School of Mathematics and Statistics, Central South University, Changsha, Hunan, China |
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Abstract: | In this paper, we consider the following fractional Schrödinger–Poisson problem: where s,t∈(0,1],4s+2t>3,V(x),K(x), and f(x,u) are periodic or asymptotically periodic in x. We use the non‐Nehari manifold approach to establish the existence of the Nehari‐type ground state solutions in two cases: the periodic one and the asymptotically periodic case, by introducing weaker conditions uniformly in with and with constant θ0∈(0,1), instead of uniformly in and the usual Nehari‐type monotonic condition on f(x,τ)/|τ|3. Our results unify both asymptotically cubic or super‐cubic nonlinearities, which are new even for s=t=1. Copyright © 2017 John Wiley & Sons, Ltd. |
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Keywords: | fractional Schrö dinger– Poisson problem Nehari‐type ground state solution asymptotically periodic asymptotically cubic or super‐cubic growth |
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