The Existence Of Solutions For A Class Of Schrodinger Equations In The Optical Lattice

In this paper, we show the existence theory for the solution of nonlinear Schr(o|¨)dingerwith nonlinearity modeling light beam propagating in a photorefractive crystal. In firstchapter, We introduce brie?y the model of the physical background, prerequisites andmain conclusions. In second chapter, we use the method of calculus of variations to provethe existence of the steady state solutions. In third chapter, we study initial value problemfor a class of Schr(o|¨)dinger equations, and prove the existence of the local solution and theglobal solution by using of contracting mapping principle and Galerkin method separately.