Multiple solutions to a linearly coupled elliptic system with critical exponents

[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.

[发布日期] 2019-12-01

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