Applications Of Fixed Point Theory To Boundary Value Problems For Dynamic Equations On Time Scales

This thesis is mainly concerned with the applications of fixed point theoryto the boundary value problems for p-Laplacian functional dynamic equations ontime scales. This thesis is composed of five chapters.In ChapterⅠ, we introduce the historical background and the recent devel-opment of problems to be studied, and main results of this thesis are also brieflyintroduced.In ChapterⅡ, we study the existence results for the p-Laplacian functionaldynamic equations on time scales by using Schaefer's fixed point theorem andnonlinear alternative of Leray-Schauder type.In ChapterⅢ, we study the eigenvalue problem for the p-Laplacian func-tional dynamic equations on time scales, and we show that the number of positivesolution of it is determined by the parameterλ.In ChapterⅣ, by using Avery-Henderson fixed point theorem and Avery-Peterson fixed point theorem, we obtain the existence results of multiple positivesolutions for the p-Laplacian functional dynamic equations on time scales.In ChapterⅤ, we combine Krasnoselskii's fixed point theorem with Leggett-Williams and get new fixed point theorems. By using the new fixed point theo-rems, we obtain multiple positive solutions for the p-Laplacian functional dynamicequations on time scales.