Quasilinearization Method For Some Impulsive Dynamic Equations On Time Scales

The periodic boundary value problems for impulsive dynamic equations on time scales are investigated by means of quasilinearization method in this paper. This dissertation focuses on two sides:one is the quasilinearization method for Periodic boundary value problems for one order impulsive dynamic equations on time scales, the other is the quasilinearization method for Periodic boundary value problems for second order impulsive dynamic equations on time scales. Main contents are as follows:Firstly, we give the basic notions connected to time scales and then a survey to the devel-opment and current state of impulsive dynamic equations, as well as the main work status. We discuss a kind of one order nonlinear impulsive dynamic equations on time scales, and gain some sufficient conditions to satisfy the rapid convergence of solutions of impulsive dynamic equations on time scales. Secondly, we discuss the nonlinear impulsive dynamic equations on time scales involving the sum of the two functions, obtain two iterative sequences by employ-ing the method of upper and lower solutions and the monotone iterative technique, two itera-tive sequences is converging to the unique solution of the equations, possessing convergence rate higher, finally, we consider second order nonlinear impulsive dynamic equations on time scales, discuss the periodic boundary value problems also by the quasilinearization method, and employing the impulsive inequality for two times, obtain rapid convergence of unique solution.