Existence Of Weak Solutions Of Boundary Value Problems For Several Classes Of Coupled Systems With Impulses

Boundary value problem of differential equation is regarded as one extremely im-portant branch of the research on mathematical basic theory and application.As the re-search on boundary value problem going deeper,impulse differential equation arouses many scholars' interests.This kind of equation is widely applied to spaceflight,engineer-ing mechanics,materials science,control technology and many other fields.Furthermore,the boundary value problem of fractional differential equation is currently one of the hot issues for mathematicians.In this dissertation,existence of weak solution of coupled system boundary value problems with impulse is studied.This dissertation consists of four chapters which follows:Chapter 1 is introduction,which introduces the research significance,research background,research status and research contents of pertinent problem.Chapter 2 introduces mountain pass theorem by which the existence of weak solution of integer-order impulsive coupled system with p-Laplacian operator is studied.Chapter 3 takes advantage of mountain pass theorem to obtain the existence and multiplicity of weak solution of fractional-order im-pulsive coupled system.Chapter 4 gives conclusions and future work of this dissertation.Two creative points in this dissertation are as follows.Firstly,p-Laplacian opera-tor is second order linear operator when p = 2,then the research problem degrades into the problem of second order linear coupled system.Thus the research in this dissertation is more general and enriches the current research results of differential system boundary value problem.Secondly,since the research of fractional-order impulsive differential sys-tem is barely studied.Base on previous research,this dissertation is concerned with the existence and multiplicity of weak solution of fractional-order impulsive coupled system.Therefore,the work in this dissertation improves the research on fractional-order differ-ential equation boundary value problem and impulsive coupled system problem to some degree.