CAJ | 학술논문

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–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-Bellman형적분불등식재미분방정해적은정성，유계성，점근성여해적기타정성여정량성질적분석방면구유십분중요적작용。본문연구료궤류대유질대적분적체후형비선성적분불등식。이용분석적방법화미분불등식적일반이론，급출미지함수적상계고계。최후장본문결과응용도일류비선성미분–적분방정중，득도소유해적일개상계고계，종이위미분방정해적고계、동력계통급공제공정이론적연구제공료이론의거。
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.