Existence Of Solutions For Several Classes Boundary Value Problems Of Dynamic Equations On Time Scales

In recent years, with the rapid development of modern science and technology, moreand more scholars are hinterested in the theory of dynamic equations on time scales.Theory of dynamic equation on time scales has been proved to be of great importance andpotential application as to embranchment of applied mathermatic. So the study of timescales has important significance in theory and application.This paper focuses on the research of existence of positive solutions of m-pointboundary value problems for three order dynamic equations on time scales, existence ofpositivesolutions for three order p-Laplacian n-point boundary value problem on timescales, three order impulsive boundary value problems with p-Laplacian on time scales,existence of solutions for periodic boundary value problems for second order impulsivedynamic equations on time scales and positive solutions of periodic boundary valueproblems for singular dynamic equations on time scales.Firstly, by the using fixed point theorem to study existence of positive solutions for anew class of mixed three order m-point boundary value problem, and the result arenew．Also, thesis gives an example of major findings．Secondly, existence of positive solutions for third-order nonlinear n-point boundaryvalue problem with p-Laplacian operator is considered. By means of five functionals fixedpoint theorem in cones,some a new results for the existence of at least three positivesolutions of the boundary value problem are abtained. Also, an exmple is worked out todemonstrate results.Again, this paper uses Avery-peterson fixed point theorem on cone to study existenceof positive solutions for a class of mixed impulsive boundary value problem withp-Laplacian. Some a new results for the existence of at least three positive solutions of theboundary value problem are abtained. Then an exmple is given to illustrate the mainresult.Finally, this paper considers the existence of solution for periodic boundary valueproblems on time scales. By means of upper and lower solutions and monotone iterativetechnique, periodic boundary value problems for second order impulsive dynamicequations on time scales and existence of positive solutions for periodic boundary valueproblems for singular second order dynamic equations are researched.Then, the sufficient conditions of the existence positive solutions for such equations have been obtained. Andthe same time, an application example is offered.