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Existence and multiplicity results for the fractional Schrodinger-Poisson systems

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 Added by Jinguo Zhang
 Publication date 2015
  fields
and research's language is English
 Authors Jinguo Zhang




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This paper is devoted to study the existence and multiplicity solutions for the nonlinear Schrodinger-Poisson systems involving fractional Laplacian operator: begin{equation}label{eq*} left{ aligned &(-Delta)^{s} u+V(x)u+ phi u=f(x,u), quad &text{in }mathbb{R}^3, &(-Delta)^{t} phi=u^2, quad &text{in }mathbb{R}^3, endaligned right. end{equation} where $(-Delta)^{alpha}$ stands for the fractional Laplacian of order $alphain (0,,,1)$. Under certain assumptions on $V$ and $f$, we obtain infinitely many high energy solutions for eqref{eq*} without assuming the Ambrosetti-Rabinowitz condition by using the fountain theorem.



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