Ground states for Chern-Simons-Schrodinger system with nonperiodic potential

The main aim in the present paper is to investigate the generalized Chern-Simons-Schrodinger system in H-1(R-2){ -delta u + V (x)u + A(0)u + sigma(2 )(j=1)A(j)(2)u = |u|(p-2)u,& part;(1)A(2 )- & part;(2)A(1 )= -1/2u(2), & part;(1)A(1 )+ & part;(2)A(2) = 0,delta A(0) = & part;(1)(A(2)|u|(2)) - & part;(2)(A(1)|u|(2)),where p is an element of (6, +infinity). Here, V is an element of C(R-2, R), V(x) = V-1(x) for x(1) > 0 and V(x) = V-2(x) for x(1) < 0, where V-1, V-2 are periodic in each coordinate direction. By giving a splitting lemma, we obtain the existence of ground state solutions for the above problem.