一类带双临界指数的凹凸非线性分数阶Schrodinger-Poisson系统的两个正解  

Two Positive Solutions for a Class of Concave-convex Fractional Schrodinger-Poisson System with Doubly Critical Exponents

作　　者：蒋维 李雨涵 李红英 JIANG Wei;LI Yuhan;LI Hongying(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《广西师范大学学报（自然科学版）》2023年第6期113-121,共9页Journal of Guangxi Normal University:Natural Science Edition

基　　金：四川省自然科学基金(2022NSFSC1816)。

摘　　要：本文研究如下带双临界指数的凹凸非线性分数阶Schrodinger-Poisson系统{(-Δ)^(s) u-∅u^(2*)_(s-3) u=u^(2*_(s)-2) u+λh(x)u^(q-2) u,x∈R^(3),(-Δ)^(s)∅=u^(2*)_(s)-1,x∈R^(3),式中:1<q<2;s∈(0,1);λ>0是实参数;h为满足一定条件的函数。利用变分法和山路定理,本文证明存在λ^(*)>0,使得当λ∈(0,λ^(*))时,该系统在D^(s,2)(R^(3))中存在1个具有负能量的局部极小正解和1个具有正能量的山路解。In this paper,the following concave-convex fractional Schrodinger-Poisson system with doubly critical exponents is investigated{(-Δ)^(s) u-∅u^(2*_(s)-3) u=u^(2*_(s)-2) u+λh(x)u^(q-2) u,x∈R^(3),(-Δ)^(s)∅=u^(2*)_(s)-1,x∈R^(3),where 1<q<2,s∈(0,1),λ>0 is a real parameter and h satisfies some certain conditions.It is showed that there existsλ^(*)>0 such that the system has a positive local minima solution with negative energy and a positive mountain-pass solution with positive energy for anyλ∈(0,λ^(*))in D^(s,2)(R^(3))by applying the Mountain Pass Theorem and variational method.

关 键 词：分数阶Schr dinger-Poisson系统 正解 山路定理 双临界指数 

分 类 号：O177.91[理学—数学]