Existence of ground state for coupled system of biharmonic Schrodinger equations

作者：Wang, Yanhua; Liu, Min; Wei, Gongming^*

来源：AIMS Mathematics, 2022, 7(3): 3719-3730.

DOI：10.3934/math.2022206

• system of Schrodinger equations
• ground state solution
• Nehari manifold
• concentration-compactness principle

In this paper we consider the following system of coupled biharmonic Schrodinger equations @@@ {Delta(2)u + lambda(1)u = u(3) + beta uv(2), @@@ Delta(2)v + lambda(2)v = v(3) +beta u(2)v, @@@ where (u, v) is an element of H-2(R-N) x H-2(R-N), 1 <= N <= 7, lambda(i) > 0(i = 1, 2) and beta denotes a real coupling parameter. By Nehari manifold method and concentration compactness theorem, we prove the existence of ground state solution for the coupled system of Schrodinger equations. Previous results on ground state solutions are obtained in radially symmetric Sobolev space H-r(2)(R-N) x H-r(2) (R-N). When beta satisfies some conditions, we prove the existence of ground state solution in the whole space H-2(R-N) x H-2(R-N).