带迭代积分的滞后型非线性积分不等式及其应用

Retarded Nonlinear Integral Inequalities with Iterative Integral and Their Applications

Growall-Bellman型积分不等式在微分方程解的稳定性,有界性,渐近性与解的其它定性与定量性质的分析方面具有十分重要的作用.本文研究了几类带有迭代积分的滞后型非线性积分不等式.利用分析的方法和微分不等式的一般理论,给出未知函数的上界估计.最后将本文结果应用到一类非线性微分一积分方程中,得到所有解的一个上界估计,从而为微分方程解的估计、动力系统及控制工程理论的研究提供了理论依据.

Growall-Bellman inequality is one of the most important inequalities investigating the qualitative and quantitative properties of solutions for differential equations such as sta-bility, boundedness, asymptotic property. In this paper, some new generalized retarded non-linear integral inequalities are discussed, and upper bound estimations of unknown functions are given by applying analysis technique and classical inequalities theories. These estimations can be employed ied to the certain nonlinear differential-integral equations. Finally, the upper bound of all solutions is given, which is the theoretic basis for the estimation of solutions, dynamical systems and control system.