Boundary Value Problems Of Impulsive Differential Equations

In recent years, the boundary value problems are math workers and other scientists concerned about one important question, which originated in nuclear physics, gas dynamics, fluid mechanics, boundary layer theory, and nonlinear optics. With in-depth study of the problem, upper and lower solution method, approximating methods, cone theory and topological degree theory has gradually become an important method to study boundary value problems. In this paper, the use of upper and lower solution method, fixed point theory, discussed the cone theory of boundary value problems for impulsive differential equations of the existence solutions. The full text is divided into four chapters.Chapter 1, outlines the boundary value problems for impulsive differential study of the history and status quo, as well as the main job of this article.Chapter 2, by using an impulsive differential inequality, we obtain a new comparison result on an impulsive periodic boundary value problems, and use-ing the method of upper and lower solutions coupled with monotone iterative technique, we obtain the existence of extremal solution about this problems.Our results improve some known results or are new.Chapter 3, discussed the three points for a class of impulsive differential equations boundary value multiple positive solutions of the problem of existence, the chapter using the cone compression and tensile cone fixed point theorem, have been three questions existence of positive solutions; improve and extend the existing non-impulsive differential equations corresponding results.Chapter 4, studies the second-order impulsive differential equations of initial value problem. The chapter use some lemma to obtain a new comparison results and theorems. And the use of these results, access to such questions the existence of extremal solutions.