Existence and asymptotic behavior of vector solutions for coupled nonlinear Kirchhoff-type systems

[摘要] This paper deals with the following linearly coupled nonlinear Kirchhoff-type system: { -(a(1) + b(1) integral(3)(R) |del u|(2) dx )Delta u + mu(1)u = f(u) + beta v in R-3, -(a(2) + b(2) integral(3)(R) |del u|(2) dx )Delta v + mu(2)v = g(v) + beta u in R-3, u,v is an element of H-1 (R-3), where a(i) > 0, b(i) >= 0, mu(i) > 0 are constants for i = 1,2, beta > 0 is a parameter and f, g is an element of C (R, R). Under the general Berestycki-Lions type assumptions on f and g, we establish the existence of positive vector solutions and positive vector ground state solutions respectively by using variational methods. We also study the asymptotic behavior of these solutions as beta -> 0(+). (C) 2017 Elsevier Inc. All rights reserved.

[发布日期] 2017-12-15

[关键词] Kirchhoff-type system;General nonlinearity;Positive vector solution;Asymptotic behavior;Pohozaev identity;Variational method