PROPERTIES OF SOLUTIONS TO NONLINEAR DYNAMIC INTEGRAL EQUATIONS ON TIME SCALES
PROPERTIES OF SOLUTIONS TO NONLINEAR DYNAMIC INTEGRAL EQUATIONS ON TIME SCALES
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发表时间：
2008
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通讯作者：
D. Pachpatte
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作者：
D. Pachpatte
本文的主要目的是研究时标上一类动力积分方程解的一些基本定性性质。在分析中所采用的工具是基于应用的Banach不动点定理和一定的不等式的时间尺度上的显式估计。技术.关于时间尺度和时间尺度上的动力学方程的一个很好的解释可以在Bohner和Peterson最近的两本书（2，3）中找到。在研究时标上的动力方程时，往往要分析与之相关的时标上的积分方程。时标上的积分方程似乎有着巨大的应用潜力，因而是最值得关注的一类。本文考虑一般非线性动力积分方程x（t）= ft，x（t），Ztt0 g（t，
The main objective of the present paper is to study some basic qualitative properties of solutions of a certain dynamic integral equation on time scales. The tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain inequality with explicit estimate on time scale. techniques. An excellent account on time scales and dynamic equations on time scales can be found in the two recent books (2, 3) by Bohner and Peterson. In the study of dynamic equations on time scales, most often the analysis turns to that of a related integral equation on time scales. It seems integral equations on time scales have an enormous potential for rich and diverse applications and thus they are most worthy of attention. In this paper we consider a general nonlinear dynamic integral equation x(t) = f t,x(t), Z t t0 g(t,