Ground state solution of semilinear Schrödinger system with local
super-quadratic conditions
Keyword(s):
In this paper, we dedicate to studying the following semilinear Schrödinger system equation*-Δu+V1(x)u=Fu(x,u,v)amp;mboxin~RN,r-Δv+V2(x)v=Fv(x,u,v)amp;mboxin~RN,ru,v∈H1(RN),endequation* where the potential Vi are periodic in x,i=1,2, the nonlinearity F is allowed super-quadratic at some x ∈ R N and asymptotically quadratic at the other x ∈ R N . Under a local super-quadratic condition of F, an approximation argument and variational method are used to prove the existence of Nehari–Pankov type ground state solutions and the least energy solutions.
2012 ◽
Vol 142
(4)
◽
pp. 867-895
◽
2010 ◽
Vol 53
(2)
◽
pp. 245-255
◽
Keyword(s):