Some Problems Of Nonlinear Impulsive Differential Equations

In this paper,the existence and uniqueness of initial boundary value solutions of several nonlinear differential equations with impulse terms are studied by using monotone iterative technique,quasilinear method and Banach compression fixed point theorem.The structure of this paper is as follows:The first chapter briefly introduces the research background of the initial boundary value problem of differential equations with impulse terms,the current situation and development trend at home and abroad,as well as the main content of this paper,the applied definitions,properties and related lemma and other preparatory knowledge.In chapter 2,we study the quasilinear method for a class of nonlinear impulsive calculus equations with nonlocal conditions.In this chapter,a set of monotone sequences are obtained by comparison principle and upper and lower solution method under appropriate assumptions,and then it is proved that the sequence converges to the unique solution of the original equation.In chapter 3,the existence and uniqueness of solutions for a class of nonlinear impulsive differential equations of p-Laplacian operator are proved.In this chapter,Schauder fixed point theorem and Banach compression mapping principle are used to obtain the existence and uniqueness of fractional nonlocal problem solutions with the p-Laplacian operator,and an example is given to verify its validity.In Chapter 4,we prove the existence and uniqueness of solutions of impulsive differential and integral equations with constant coefficients and anti-periodic boundary conditions.In this chapter,the existence and uniqueness of solutions for nonlocal problems with multivalued Mittag-Leffler function are obtained by transforming the impulsive differential equations into equivalent Volterra integral equations,then by using the Banach contraction mapping principle and the Krasnoselskii Fixed-point theorem,and give some examples.Finally,based on the existing research foundation,this paper introduces the future research work.