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The fractional Schr\"{o}dinger-Poisson systems with infinitely many solutions

Tiankun Jin|Zhipeng Yang
대한수학회 (The Korean Mathematical Society)|2020.03|대한수학회지 (Journal of the KMS)|제57권 제2호|pp. 489-506|DOI 10.4134/JKMS.j190156

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키워드

variational methodfountain theoremFractional Schr\"{o}dinger-Poisson system
주제분류수학

초록

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

Abstract

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

참고문헌 (35)

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