Ground State Solutions to a Critical Nonlocal Integrodifferential System

Min Liu, Zhijing Wang and Zhenyu Guo

Advances in Mathematical Physics, 2018, vol. 2018, issue 1

Abstract: Consider the following nonlocal integrodifferential system: LKu+λ1u+μ1u2⁎-2u+Gu(x,u,v)=0000 in Ω, LKv+λ2v+μ2v2⁎-2v+Gv(x,u,v)= in Ω, u=, v= 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 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.

Date: 2018
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https://doi.org/10.1155/2018/4312083

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:4312083

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