The Existence Of The Global Solution To A Class Of Fourth-Order Nonlinear Schrodinger Equation

Nonlinear Schr(?)dinger equations are fundamental equations of the quantum mechanics, which originate from the quantum field theory, specially in Hartree-Fock theory. In recent years, the nonlinear Schr(?)dinger equations have received a great deal of attention from mathematicians. In the field of nonlinear optics, some simplified models lead to certain nonlinear Schr(?)dinger equations.In this paper we study the initial boundary problem of a class of nonlinear Schr(?)dinger equationsWe obtain the existence of solutions. Firstly in chapter two, we introduce the B-G inequation, which is important in the proof of the global existence of solutions. Secondly, we testify the boundedness of the solutions in chapter three, which satisfy the condition of the B-G inequation. Finally in chapter four, by using the operator semigroup theory and B-G inequation, we gain the global existence of solutions.