具外部位势分数阶Choquard方程的基态解

Ground states for fractional Choquard equations with external potential

研究具外部位势非自治分数阶Choquard方程:{(-?)~su+mu+V(x)u=(1+a(x))(I_α*|u|p)|u|^(p-2)u,x∈R^N u(x)→0,当|x|→∞时,基态解的存在性.利用Nehari流形技巧、集中紧性原理和山路引理得到了基态解的存在性.

We consider the following fractional Choquard equation {（-？）^su＋mu＋V（x）u=（1＋a（x））（Iα＊｜u｜p）｜u｜^（p-2）u,x∈R^N u（x）→0,as｜x｜→∞where V（x） is a bounded external scalar function, In is a Riesz potential, s E （0, 1）, ~ E （0, N） and p E [2, c~）. As a（x） satisfies the appropriate condition, and does not have any symmetry condition, we obtain the existence of ground state solutions for the equation by using Nehari mainfold technique, Concentration-compactness principle and the Mountain Pass theorem.