Concentrating phenomenon for fractional nonlinear Schrödinger-Poisson system with critical nonlinearity

2019/06/27 by Teng, Kaimin
#35B38 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.11563

Abstract

In this paper, we study the following fractional Schrödinger-Poisson system \ ε^2s(-Δ)^su+V(x)u+ϕu=g(u) · amp; \hboxin ℝ³, ε^2t(-Δ)^tϕ=u², u · gt;0 · amp; \hboxin ℝ³, . where s,t∈(0,1), ε>0 is a small parameter. Under some suitable assumptions on potential function V(x) and critical nonlinearity term g(u), we construct a family of positive solutions u_ε∈ H^s(ℝ³) which concentrates around the global minima of V as ε→0.

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