Ground State Solutions to a Critical Nonlocal Integrodifferential System - Min Liu; Zhijing Wang; Zhenyu Guo (Advances in Mathematical Physics)
Consider the following nonlocal integrodifferential system: LKu+λ1u+μ1u2⁎-2u+Gu(x,u,v)=0  in  Ω,  LKv+λ2v+μ2v2⁎-2v+Gv(x,u,v)=0  in  Ω,  u=0,  v=0  in  RN∖Ω, where LK is a general nonlocal integrodifferential operator, λ1,λ2,μ1,μ2>0, 2⁎≔2N/N-2s is a fractional Sobolev critical exponent, 0<s<1, N>2s, G(x,u,v) is a lower order perturbation of the critical coupling term, and Ω is an open bounded domain in RN with Lipschitz boundary. Under proper conditions, we establish an existence result of the ground state solution to the nonlocal integrodifferential system.