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Existence of semiclassical solutions for some critical Schrödinger–Poisson equations with potentials
Nonlinear Analysis ( IF 1.4 ) Pub Date : 2020-04-03 , DOI: 10.1016/j.na.2020.111874
Minbo Yang

In this paper we are interested in the existence of semiclassical solutions for the critical Schrödinger–Poisson equations with multiple potentials. Under suitable assumptions on the potentials, we are able to prove the existence of semiclassical solutions (uε,ϕε) with maximum points xε of uε concentrating at a special set CP characterized by some of the potentials. Moreover, for any sequence xεx0CP, by setting vε(x)uε(εx+xε), the ground solutions vε convergence strongly in H1(R3) to a ground state solution v of Δv+V(x0)v=P(x0)g(v)+Q(x0)|v|4v,inR3.



中文翻译:

具有势能的某些关键Schrödinger-Poisson方程的半经典解的存在

在本文中,我们对具有多个潜在势的临界Schrödinger-Poisson方程的半经典解的存在性感兴趣。在潜在的适当假设下,我们能够证明半经典解的存在üεϕε 最高分 Xεüε 专注于一个特殊的场景 CP具有某些潜力。而且,对于任何顺序XεX0CP, 通过设置 vεXüεεX+Xε,地面解决方案 vε 强烈融合 H1个[R3 到基态解决方案 v-Δv+VX0v=PX0Gv+X0|v|4v[R3

更新日期:2020-04-03
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