The Existence Of Global Solutions For A Class Of Schr(?)dinger Equations

In this paper we study the Cauchy problem of a class of Schrodingerequation and the initial boundary value problemWe obtain the existence of solutions and the blow-up of solutions for the problemwhen1＜p＜∞,n=1,2；1＜p≤(n+2)／(n-2),n≥3.Firstly, by using the potential wellmethod we prove the global existence of solutions of the Cauchy problem, thenwe use the energy method discuss the blow-up of solutions of the problem.Secondly, by introducing a family of potential wells, the global existence ofsolutions of the initial boundary value problem are studied. Finally we discuss theblow up phenomenon of solutions. And the known results are generalized andimproved essentially.