Existence of minimizers for some coupled nonlinear Schrödinger equations

Abstract

The existence and nonexistence of minimizers for two minimizing problems are considered. These problems are related to three coupled nonlinear Schrödinger equations which appear in the field of nonlinear optics. We observe the relationship between two minimizing problems and also study the asymptotic behavior when the coefficient standing for the nonlocal nonlinearity tend to 0.