Boundary Value Problems For Nonlinear Differential Equations

As we know, nonlinear diferential equations have been applied in many area. Nonlinearimpulsive diferential equations have become more important in some mathematical modelsof real processes phenomena studied in physics, chemical technology, population dynamics,biotechnology and economics. And fourth-order value problems are useful for material me-chanics because the problems usually characterize the deformations of an elastic beam. Sononlinear diferential equations have aroused international widespread attentions. The mainwork of this paper includes the following four parts:In the first chapter of introduction, we introduce the history and main results of thisthesis.In the second chapter, using Schauder fixed point theorem, upper and lower solutionmethod,monotone iterative technique and corollaries of Banach contraction principle,we mainlydiscuss second order impulsive integro-diferential equations with deviation arguments,whichinclude periodic boundary value,anti-periodic boundary value conditions.In the third chapter, we are concerned with the nonlinear mixed impulsive integro-diferential equations with the derivative u and deviating arguments in Banach space E. weobtain some conditions on existence and uniqueness of solutions.In the last chapter,we main study fourth-order boundary value problems, Using Schauderfixed point theorem, upper and lower solution method,monotone iterative technique and corol-laries of Banach contraction principle, we obtain some conditions on existence and uniquenessof solutions or positive solutions.Finally,we make a summary and express my thanks.