Ground State Solutions to a Critical Nonlocal Integrodifferential System. (8th August 2018) - Liu, Min; Wang, Zhijing; Guo, Zhenyu
Abstract : Consider the following nonlocal integrodifferential system:L K u + λ 1 u + μ 1 u 2 ⁎ - 2 u + G u ( x, u, v ) = 0 i n Ω, L K v + λ 2 v + μ 2 v 2 ⁎ - 2 v + G v ( x, u, v ) = 0 i n Ω, u = 0, v = 0 i n R N ∖ Ω, whereL K is a general nonlocal integrodifferential operator, λ 1, λ 2, μ 1, μ 2 > 0, 2 ⁎ ≔ 2 N / N - 2 s is a fractional Sobolev critical exponent, 0 < s < 1, N > 2 s, G ( x, u, v ) is a lower order perturbation of the critical coupling term, andΩ is an open bounded domain inR N with Lipschitz boundary. Under proper conditions, we establish an existence result of the ground state solution to the nonlocal integrodifferential system.