Existence Of Positive Solutions Of Dynamic Equations On For Boundary Problems And Periodic Boundary Problems On Time Scales

With the development of modern science and technology, people have proposed a great many problems about differential and difference equations in natural science and social science, and some results are gained. The differential equations introduce the difference equations with polarized. Many of the nature of the differential equations have been kept. But, it is impied there are so many differences between them. The theory of time scales can unify differential and difference, which pioneers a new mathematical area-dynamic equations. Firstly, dynamic equations on time scales deel with the differential equations and difference equations as its sepcial circumstances and reveals the essence of continuous and discrete cases. It avoids repeat study, but also contains many other cases. Secondly, it exists many time scales except for Real set and Integer set in set R , so the study of time scales has important significance in theory and application. In addition, theory of dynamic equations on time scales has been and are being proved to be of great importance and potential application as to embranchment of applied mathematic. In application, dynamic equations has a wide base in nature, for instance, epidemic models, neuronal network model and insectile numbers models. Except these applications in biology, the mathematical tool has been used to prove calculational mode about stock market.In this thesis, existence of positive solutions for dynamic equations boundary value problems and periodic boundary problems on time scales are researched.Firstly, eigenvalue intervals for a class of second order nonlinear dynamic equations on time scales are researched, a series of sufficient conditions for positive solutions are established. Secondly, this paper discusser positive solutions of two classes of third order nonlinear dynamic equations on time scales and some conditions are obtained.Finally, this paper discusses positive solutions to nonlinear first order PBVPs with parameter on time scales.