Multiple solutions to a linearly coupled elliptic system with critical exponents

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:480

Article

Wu, Huiling¹ 

[1] Minjiang Univ, Coll Math & Data Sci, Fuzhou 350108, Fujian, Peoples R China

关键词: Nonlinear elliptic system;    Critical exponent;    Positive solution;    Asymptotic behavior;   

DOI  :  10.1016/j.jmaa.2019.123380

来源: Elsevier

【 摘 要 】

We are concerned with the linearly coupled elliptic system with critical exponents {-Delta u + a(x)u = vertical bar u vertical bar(2*-2)u +mu vertical bar u vertical bar(p-2) u + lambda u, x epsilon R-N, -Delta v + b(x)v = vertical bar v vertical bar(2*-2)v +nu vertical bar v vertical bar(p-2) v + lambda u, x epsilon R-N, u, v epsilon H-1(R-N), where N >= 3, 2 < p, q < 2* = N2/N-2, mu, nu and lambda are nonnegative constants, and a(x), b(x) are positive periodic functions. The existence of a positive ground state and a higher energy solution of this system is proved using variational methods. Additionally, the asymptotic behavior of these solutions as lambda > 0(+) is obtained. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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