一类非局部拟线性椭圆方程组无穷多解的存在性  

Infinitely Solutions for a Class of Nonlocal Quasilinear Elliptic Equations

作　　者：王倩 陈林 汤楠 Wang Qian;Chen Lin;Tang Nan(College of Mathematics and Statistics,Yili Normal University,Xinjiang Yining 835000;Institute of Applied Mathematics,Yili Normal University,Xinjiang Yining 835000)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]伊梨师范大学应用数学研究所,新疆伊宁835000

出　　处：《数学物理学报（A辑）》2022年第3期767-774,共8页Acta Mathematica Scientia

基　　金：伊犁师范大学博士科研启动基金(2017YSBS08)。

摘　　要：该文运用对称山路引理研究一类拟线性椭圆方程组{M(∫_(RN)(|▽_(u)|^(p)+v(x)|u|^(p)dx)(-△_(p)U+V(x)|u|^(p-2)u)=σd^(-1)F_(u)(x,u,v)+λ|u|^(q-2)u,M(∫_(RN)(|▽_(v)|^(p)+v(x)|v|^(p)dx)(-△_(p)v+V(x)|v|^(p-2)v)=σd^(-1)F_(v)(x,u,v)+λ|u|^(q-2)v,u,v∈W^(1,p)(R^(N)),x∈R^(N)无穷多解的存在性,其中M(s)=s^(k),k>0,N≥3,p>1,p(k+1)<q≤d<p^(*)≤N无穷多解的存在性,其中M(s)=s,k>0,N≥3,p>1,p(k+1)<q≤d<p²≤N(当p<N时,p^(*)=Np/(N-p);当p=N时,p^(*)=∞),λ,μ>0∈R^(N),权函数V(x)∈C(R^(N))满足某些给定的条件.In this paper,we study the existence of multiple solutions for a class of nonlocal quasilinear elliptic problem{M(∫_(RN)(|▽_(u)|^(p)+v(x)|u|^(p)dx)(-△_(p)U+V(x)|u|^(p-2)u)=σd^(-1)F_(u)(x,u,v)+λ|u|^(q-2)u,M(∫_(RN)(|▽_(v)|^(p)+v(x)|v|^(p)dx)(-△_(p)v+V(x)|v|^(p-2)v)=σd^(-1)F_(v)(x,u,v)+λ|u|^(q-2)v,u,v∈W^(1,p)(R^(N)),x∈R^(N)where M(s)=s^(k),k>0,N≥3,p>1,p(k+1)<q≤d<p^(*)≤N,λ,μ>0,σ∈R^(N),and in which p^(*)=Np/(N-p),and p^(*)=∞if p=N.The weight functionV(x)∈C(R^(N))satisfy some conditions.

关 键 词：椭圆方程 对称山路引理 (PS)条件 

分 类 号：O175.2[理学—数学]