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Existence of infinitely many small solutions for fractional Schrödinger-Poisson systems with sign-changing potential and local nonlinearity

  • Received: 07 July 2020 Accepted: 26 August 2020 Published: 07 September 2020
  • MSC : 35J60, 35J20

  • In this paper, we prove the existence of infinitely many small solutions for the following fractional Schr?dinger-Poisson system $ \begin{equation*} \left\{ \begin{array}{ll} (-\Delta)^s u+V(x)u+\phi u = f(x,u),&x\in\mathbb{R}^3,\\ (-\Delta)^t\phi = u^2,& x\in\mathbb{R}^3, \end{array} \right. \end{equation*} $ where $(-\Delta)^\alpha$ denotes the fractional Laplacian of order $\alpha\in(0, 1)$ and $V$ is allowed to be sign-changing. We obtain infinitely many small solutions via a dual method. Our main tool is a critical point theorem which was established by Kajikiya.

    Citation: Zonghu Xiu, Shengjun Li, Zhigang Wang. Existence of infinitely many small solutions for fractional Schrödinger-Poisson systems with sign-changing potential and local nonlinearity[J]. AIMS Mathematics, 2020, 5(6): 6902-6912. doi: 10.3934/math.2020442

    Related Papers:

  • In this paper, we prove the existence of infinitely many small solutions for the following fractional Schr?dinger-Poisson system $ \begin{equation*} \left\{ \begin{array}{ll} (-\Delta)^s u+V(x)u+\phi u = f(x,u),&x\in\mathbb{R}^3,\\ (-\Delta)^t\phi = u^2,& x\in\mathbb{R}^3, \end{array} \right. \end{equation*} $ where $(-\Delta)^\alpha$ denotes the fractional Laplacian of order $\alpha\in(0, 1)$ and $V$ is allowed to be sign-changing. We obtain infinitely many small solutions via a dual method. Our main tool is a critical point theorem which was established by Kajikiya.


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