GROUND STATES OF NONLINEAR SCHRODINGER SYSTEMS WITH PERIODIC OR NON-PERIODIC POTENTIALS

摘要

In this paper we study a class of weakly coupled Schrodinger system arising in several branches of sciences, such as nonlinear optics and Bose-Einstein condensates. Instead of the well known super-quadratic condition that lim(vertical bar z vertical bar -infinity )F(x,z)/vertical bar z vertical bar(2) = infinity uniformly in x, we introduce a new local super-quadratic condition that allows the nonlinearity F to be super-quadratic at some x is an element of R-N and asymptotically quadratic at other x is an element of R-N. Employing some analytical skills and using the variational method, we prove some results about the existence of ground states for the system with periodic or non-periodic potentials. In particular, any nontrivial solutions are continuous and decay to zero exponentially as vertical bar x vertical bar - infinity. Our main results extend and improve some recent ones in the literature.