Iterative Solution And Variable Order Solution For Boundary Value Problems Of Nonlinear Differential Equations

Nonlinear differential equation boundary value problems come from the applied mathematics, control theory, engineering, biology, physics and many other applied subjects. In recent years, the study applying nonlinear functional analysis about the existence of solutions for the differential equation boundary value problems has been attracting the attention of many scholars. This dissertation is mainly involved the existence of the solutions for several classes of nonlinear differential equation boundary value problems. In this paper, we mainly apply the iterative technique, fixed point theory, lattice and the upper and lower solution method, etc.The dissertation is divided into five chapters.In Chapter I, we briefly introduce the research work and some basic concepts and corresponding theorems.In Chapter II, by applying the iterative technique and the nonlinear monotonic operator, we study the existence and uniqueness of symmetric positive solution for a class of higher order singular differential equation boundary value problem. With the case that f(t, u) may be singular at u= 0, t=0(and/or t=1), we obtain the existence and uniqueness of symmetric positive solution for the following higher order boundary value problem At the same time, we also give the corresponding error estimates of the symmetric positive solutions.In Chapter III, with the upper and lower solutions and different iterative schemes,we mainly study the existence of positive solutions for the following third-order differential equation with nonlinear boundary conditionsIn Chapter IV, we mainly consider the existence of positive solutions for the fractional order difference equation with q-differenceIn Chapter V, by applying a fixed point theorem in the lattice, we mainly study the existence of sign-changing solution for the following third-order differential equation boundary value problem...