具有无穷多个解的分数阶schrÖdinger-poisson系统

Pub Date : 2020-01-01 DOI:10.4134/JKMS.J190156

T. Jin, Zhipeng Yang

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引用次数: 7

摘要

。本文研究了超立方分数阶Schr¨odinger-Poisson系统无穷多个大能量解的存在性。我们从众所周知的Ambrosetti-Rabinowitz型条件出发，考虑了非线性的不同的超线性增长假设。利用喷泉定理，在此情况下得到了三个不同的存在性结果，所有这些结果都将半线性Schr¨odinger-Poisson系统的一些结果推广到非局部分数型情况。

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THE FRACTIONAL SCHRÖDINGER-POISSON SYSTEMS WITH INFINITELY MANY SOLUTIONS

. In this paper, we study the existence of inﬁnitely many large energy solutions for the supercubic fractional Schr¨odinger-Poisson sys- tems. We consider diﬀerent superlinear growth assumptions on the nonlinearity, starting from the well-know Ambrosetti-Rabinowitz type condi- tion. We obtain three diﬀerent existence results in this setting by using the Fountain Theorem, all these results extend some results for semelinear Schr¨odinger-Poisson systems to the nonlocal fractional setting.

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