带有一般位势的分数阶薛定谔-泊松系统Nehari-Pohozaev类型基态解的存在性

Existence of ground state solutions of Nehari-Pohozaev type for fractional Schrodinger-Poisson systems with a general potential

研究了下述带有一般位势的分数阶薛定谔-泊松系统的基态解的存在问题(-Δ)su+V(x)u+φu=f(u),inR^3,(-Δ)tφ=u 2,inR^3,其中(-Δ)s和(-Δ)t代表了分数阶拉普拉斯,0<s≤t<1而且2s+2t>3,位势V(x)弱可微,f∈C(ℝ,ℝ).在位势函数V(x)以及非线性项f(u)满足一定假设下,利用Jeanjean单调技巧和全局紧性引理,得到了该问题Nehari-Pohozaev型基态解的存在性.

In this paper,we consider the existence of ground state solutions to the following fractional Schr dinger-Poisson systems with a general potential(-Δ)su+V(x)u+φu=f(u),in R^3,(-Δ)tφ=u 2,in R^3,where(-Δ)s and(-Δ)t denote the fractional Laplacian,0<s≤t<1 and 2s+2t>3,the potential V(x)is weakly differentiable and f∈C(ℝ,ℝ).Under some assumptions on potential V(x)and f(u),a nontrivial ground state solutions of Nehari-Pohozaev type(u,φ)is established through using a subtle approach developed by Jeanjean and global compactness Lemma.