On critical systems involving fractional Laplacian

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Guo, Zhenyu^1,2  Luo, Senping²  Zou, Wenming² 

[1] Liaoning Shihua Univ, Sch Sci, Fushun 113001, Peoples R China

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

关键词: Ground state;    Nehari manifold;    Fractional-Sobolev critical exponent;   

DOI  :  10.1016/j.jmaa.2016.08.069

来源: Elsevier

【 摘 要 】

Consider the following non-local critical system {(-Delta)(s)u - lambda(1)u = mu(1)vertical bar u vertical bar(2)*(-2)u + alpha gamma/2* vertical bar u vertical bar(alpha-2)u vertical bar v vertical bar(beta) in Omega, (-Delta)(s)v - lambda(2)v = mu(2)vertical bar v vertical bar(2)*(-2)v + beta gamma/2* vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta-2)v in Omega, u = 0, v = 0 in R-N\Omega, where (-Delta)(s) is fractional Laplacian, 0 < s < 1 and all lambda(1), lambda(2), mu(1), mu(2), gamma > 0, 2(*) := 2N/N - 2s is a fractional Sobolev critical exponent, N > 2s, alpha, beta > 1, alpha + beta = 2(*), and Omega is an open bounded domain in R-N with Lipschitz boundary. Under proper conditions, we establish the existence result of the ground state solution to system (0.1). (C) 2016 Elsevier Inc. All rights reserved.

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