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Oscillatory and Asymptotic Behavior of Dynamic Equations and Existence of Solutions for Impulsive Equations on Time Scales

Author: SunLiJie
Tutor: YangJun
School: Yanshan University
Course: Operational Research and Cybernetics
Keywords: Time scales Dynamic equation Impulsive Oscillation Existence Boundary value problems
CLC: O175.8
Type: Master's thesis
Year: 2010
Downloads: 11
Quote: 1
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Abstract


In real life, when we handle various problems in the natural phenomena with mathematics method, not only run into the continuous problems, but also run into the discrete problems. The theory of time scales can just unify continuous and discrete cases, which pioneers a new mathematical area. This theory not only unifies differential and difference equations, but also reveals the essence of continuous and discrete cases, avoids repeat study. The prominent peculiarity of time scales is unification and generalization, so the study of time scales has important significance in theory and application.As a transient phenomenon, the impulsive phenomenon in modern science and technology areas of practical problems exists in common, their models are often boiled down to the impulsive differential equations. The most prominent feature of impulsive equation is able to fully consider the influence of the instantaneous state of mutant phenomenon, deeper and more accurately reflect the variation of things. In recent years, the impulsive equations in space technology and information science, life science and medicine, economic and other fields have important application.In this thesis, oscillatory and asymptotic behavior of dynamic equations and existence of solutions of impulsive dynamic equations on time scales are researched.Firstly, oscillation of a class of second order neutral dynamic equations on time scales are discussed, a series of sufficient conditions to satisfy oscillations of the equations are gained. At the same time, a example is given.Secondly, some sufficient conditions for oscillatory and asymptotic behavior of a class of third order neutral variable delay dynamic equations on time scales are established. These results are illustrated by examples.The existence of solutions for a class of first order delay impulsive dynamic equations on time scales are considered. By using the Sadovskii fixed point theorem, some sufficient conditions for solutions of the equation are established. At the same time, a example is given.Finally, the existence of positive solutions for two classes of second order impulsive boundary value problems on time scales are studied. By employing the fixed point theorems, some sufficient conditions to satisfy existence of positive solutions of these equations are established. At the same time, a example is given.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
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