Positive Solutions Of Two Tapes Of Boundary Value Problem Of Nonlinear Impulsive Differential Equations

In the 1950s,nonlinear functional analysis has initially formed a complete theo-retical system.As an important part of it,the nonlinear differential integral problem has been paid much attention by both the domestic and foreign mathematics circles and the whole natural science community because of its " Can be a good explanation of the effectiveness of many natural phenomena."From the development point of view,the nonlinear differential-integral problem comes from the application of mathematics and physics in many aspects of the application of mathematical physics and engineering and other applied disciplines have a very important The application of value,the signif-icance of the study of this problem lies in this.With the physical,aerospace technology,biotechnology and other areas of the continuous emergence of real problems,nonlinear functional analysis has become an important theoretical tool to solve these nonlinear problems,The existence and multiplicity of solutions of nonlinear differential integral equations have become one of the important research topics.It can clearly describe the various nonlinear problems in the applied disciplines such as physics,chemistry and economy.In recent years,due to the boundary value problem in chemical engineering,ther-modynamics,population dynamics,heat conduction,plasma physics in a variety of applications,with the boundary conditions of the boundary value problem is widely concerned about the differential equation boundary value problem The existence of d-ifferential equations is usually combined with boundary conditions and transformed into integral equations to find the fixed points of the integral equation.In this paper,we study the nonlinear differential equations with integral boundary conditions on t-wo Banach spaces,which enrich the differential equations The theoretical study of the positive solution of the boundary value problem is as follows:In the first chapter,we mainly introduce the research background and the research status of the integral boundary value differential equation,and give some basic defini-tions,basic properties and some important fixed point theorems for the integral bound-ary value problem.In the second chapter,we study the existence of positive solutions for the third order nonlinear differential-integral equations with monotone homomorphism andintegral boundary conditions in real Banach spaces.is considered.Where I =[0,1],J =?0,1?,J'=J\{t₁,t₂,…,t_m}.Some suffi-cient conditions for the existence of positive solutions to this boundary value problem of nonlinear integro-differential equation are established by nonlinear alternative of fixed-point index theorem and Guo-Krasnosel'skii fixed point theorem on cones,some examples are provided to illustrate our main results.In the third chapter,by constructing Green's function,we study the positive so-lutions of integral boundary value problem for the integro-differential equations with p-Laplacianwhere,?_p is is p-Laplacian operator,that is,?_p{u)= |u|^p-2u?p>1?,?_p^-1?u?= ?_q?u??1/p+1/q=1?.Some sufficient conditions for the existence of positive solutions to this boundary value problem of nonlinear integro-differential equation are established by nonlinear alternative of fixed-point index theorem and Guo-Krasnosel'skii fixed point theorem on cones,some examples are provided to illustrate our main results.