Study on a Generalized Nonlinear Equation

Using leray-Schauder fixed point theorem with usual sobolev H∞ and certain weighed sobolev spaces build an initial value problem of a class of the extended nonlinear equation. The way of solution this equation can transfer to solution a fixed point φ of integrality uninterrupted figure had been proved. The global existing and uninterrupting of all fixed pointsφ exist in Bx01 had been proved by using Leray-Schauder fixed point theorem. The result shows that solution of this equation can astringency to solution of initial value problem, get one and only smooth solution of this equation.