Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) condition

Tiankun Jin; Tiankun Jin

doi:10.3934/math.2021525

AIMS Mathematics

2021, Volume 6, Issue 8: 9048-9058. doi: 10.3934/math.2021525

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Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) condition

Tiankun Jin ^,

College of Teacher Education, Daqing Normal University, Daqing 163000, China

Received: 22 January 2021 Accepted: 02 June 2021 Published: 17 June 2021
MSC : 35J20, 35A01, 58E05

In this paper, we study the following fractional Schrödinger-Poisson system

$ \begin{equation*} \begin{cases} (-\Delta)^su+V(x)u+\phi u = f(x, u)& x\in\mathbb{R}^3, \\ (-\Delta)^s\phi = u^2& x\in\mathbb{R}^3. \end{cases} \end{equation*} $

Using the variant fountain theorem introduced by Zou ^[32], we get the existence of infinitely many large energy solutions without the Ambrosetti-Rabinowitz's 4-superlinearity condition. Recent results from the literature are extended and improved.
- fractional Schrödinger-Poisson equation,
- variant fountain theorem,
- variational methods
Citation: Tiankun Jin. Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) condition[J]. AIMS Mathematics, 2021, 6(8): 9048-9058. doi: 10.3934/math.2021525

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Abstract

In this paper, we study the following fractional Schrödinger-Poisson system

$ \begin{equation*} \begin{cases} (-\Delta)^su+V(x)u+\phi u = f(x, u)& x\in\mathbb{R}^3, \\ (-\Delta)^s\phi = u^2& x\in\mathbb{R}^3. \end{cases} \end{equation*} $

Using the variant fountain theorem introduced by Zou ^[32], we get the existence of infinitely many large energy solutions without the Ambrosetti-Rabinowitz's 4-superlinearity condition. Recent results from the literature are extended and improved.

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