Maximum Principles For Dynamic Equations On Time Scales

In this paper,we consider the second elliptic dynamic operators on time s-cales.We establish basic generalized maximum principles under the△measure and the▽measure, and apply them to obtain the uniqueness of Dirichlet bound-ary value problems for dynamic elliptic equations.In the first chapter of this paper,we introduce the history background and the main work of this article.In the second chapter,we present the basic knowledge of time scales, mainly about on the definition of△measure and▽measure on the time scales, the definition and properties of Lebesgue integral on time scales, the definition and some properties of weak solution on the time scale, which provide the basis proof behin for maximum theoremThird chapter discussed the generalized maximum principles under the△measure on the time scale we apply them to obtain the uniqueness of Dirichlet boundary value problems for dynamic elliptic equations. The disproof method which we use mainly reference from 《the Elliptic Partial Differential Equations of Second Order》 by David Gilbarg.The fourth chapter discussed the generalized maximum principles under the▽measure on the time scale which is similar to the third chapter.