Existence and concentration of solutions for a fractional Schrodinger-Poisson system with discontinuous nonlinearity

In this paper, we study the following fractional Schrodinger-Poisson system with discontinuous non-linearity: {epsilon(2s)(-Delta)su+V(x)u+phi u=H(u-beta)f(u),in R-3, epsilon(2s)(-Delta)(s)phi=u(2), in R-3, u>0,inR(3), where epsilon>0 is a small parameter,s is an element of(3/4,1),beta>0,His the Heaviside function, (-Delta)(s)u is the fractional Lapla-cian operator,V:R-3 -> R is a continuous potential andf:R -> Ris superlinear continuous nonlinearity with subcritical growth at infinity. By using non smooth analysis, we investigate the existence and concentration of solutions for the above problem. Moreover, we obtain some properties of these solutions, such as convergence and decay estimate