Studies On The Time Scale Symmetric Solutions Of Boundary Value Problems For Generalized

The theory of dynamic equations on time scales, was introduced by Stefan Hilger in order to unify differential and difference equations. In this paper, we study the generalized symmetric positive solutions of boundary value problems on time scales. Therefore, some basic definitions and lemmas on time scales are introduced in chapter1,and the definition of generalized symmetric time scales and generalized symmetric function are well defined.In chapter2, by using the fixed-point theorem in cones, necessary and sufficient conditions for the existence of generalized symmetric positive solutions of two-order boundary value problems are obtained. In this process, some useful estimates on the size of solution and its derivative are also acquired. The additional interesting points here are that the nonlinear term f is involved with derivatives explicitly and the model is equipped with p-Laplacian operator.In chapter2, by using the Avery and Peterson fixed-point theorem in cones, we consider the existence of multiple generalized symmetric positive solutions for the2m-point boundary value problems with one-dimensional p-Laplacian on time scales subject to the boundary conditions The interesting points here are that the number of generalized symmetric pos-itive solutions is countable and the nonlinear term f involving with derivatives explicitly.