Infinitely Many Radial Solutions for the Fractional Schrodinger-Poisson Systems

Volume 9, Issue 6, pp 3808--3821 http://dx.doi.org/10.22436/jnsa.009.06.30

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Authors

Huxiao Luo - School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P. R. China. Xianhua Tang - School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P. R. China.

Abstract

In this paper, we study the following fractional Schrödinger-poisson systems involving fractional Laplacian operator \[ \begin{cases} (-\Delta)^s + v(|x|)u + \phi(|x|,u)=f(|x|,u),\,\,\,\,&\ x\in \mathbb{R}^3,\\ (-\Delta)^t \phi = u^2,\,\,\,\,&\ x\in \mathbb{R}^3, \qquad (1) \end{cases} \] where \((-\Delta)^s(s \in (0; 1))\) and \((-\Delta)^t(t \in (0; 1))\) denotes the fractional Laplacian. By variational methods, we obtain the existence of a sequence of radial solutions.

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Keywords

• Fractional Schrödinger-poisson systems
• radial solution
• variational methods.

MSC

•  35J60
•  35S30
•  35J20
•  47J30

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