Open AccessGround state solution of semilinear Schrödinger system with local super-quadratic conditions
Author(s) -
Jing Chen,
Yiqing Li
Publication year - 2021
Publication title -
electronic journal on the qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2021.1.85
Subject(s) - algorithm , computer science
In this paper, we dedicate to studying the following semilinearSchrödinger system e q u a t i o n *- Δ u + V 1 ( x ) u = Fu( x , u , v )a m p ;m b o x i n ~RN ,r - Δ v + V 2 ( x ) v = Fv( x , u , v )a m p ;m b o x i n ~RN ,r u ,v ∈ H 1 (RN ) ,e n d e q u a t i o n *where the potential V i are periodic in x , i = 1 , 2 , the nonlinearity F is allowed super-quadraticat some x ∈ R N and asymptotically quadratic at the other x ∈ R N . Under a local super-quadratic condition of F , anapproximation argument and variational method are used to prove the existence of Nehari–Pankov type ground state solutions and the least energysolutions.