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

The theory of dynamic equations on time scales is a fairly new subject ofmathematics that has recently attracted a lot of attention, and research in this area israpidly growing. This theory not only unifies the study of differential and differenceequations, reveals the essence of continuous and discrete cases, avoids proving resultstwice, but also reveals more complex dynamic system. The prominent peculiarity of timescales is unification and genetalization, and theory of dynamic equation on time scales hasbeen proved to be of great importance and potential application as to embranchment ofapplied mathermatic. So the study of time scales has important significance in theory andapplication.In this thesis, existence of solutions for boundary value problems of dynamicequations on time scales is researched.Firstly, by using the fixed point theorem and Green function of boundary valueproblem, we discuss the existence of solutions for the second order m-point boundaryvalue problem on time scales. Then an example is provided to illstuate it.Secondly, existence of solutions for the third order implusive boundary valueproblems on time scales is studied. We construct the Green function of the boundary valueproblems, and then get the sufficient conditions for existence of solutions of boundaryvalue problems via the fixed point theorem.Again, successive iteration and positive solution for second order four pointboundary value problems with a p-Laplacian operator on time scale is discussed, byconstructing a completely continuous operator and a monotone iterative sequence. Thenwe give an example to explain.Further, successive iteration and positive solution for second order mixed implusiveboundary value problems on time scales is researched, we get the sufficient conditions forexistence of solutions of boundary value problem. And then we give an example toillustrate it.Finally, we consider the existence of solution for fourth order four point boundaryvalue problems on time scales, and get the sufficient conditions for existence of solutionsof boundary value problem by using the upper and lower solution and the Green function.