摘要
由于Gronwall类积分不等式是研究微分方程和积分方程解的存在性、有界性、唯一性、稳定性和不变流型等定性性质的重要工具,许多数学家研究了Gronwall类积分不等式的各种推广形式及其应用.随着积分不等式理论和脉冲微分方程理论的发展,人们又开始研究非连续函数积分不等式.使用分析技巧和数学归纳法给出了一类非连续函数积分不等式中未知函数的估计,可以用所得结果研究文献(Nonlinear Anal.,2007,66:498-508.)中的非连续函数不等式,把所得结果用于研究脉冲微分方程解的上界.
Being an important tool in the study of existence,uniqueness,boundedness,stability,invariant manifolds and other qualitative properties of solutions of differential equations and integral equations,various generalizations of Gronwall inequality and their applications have attracted great interests of many mathematicians.Along with the development of the theory of integral inequalities and the theory of impulsive differential equations,more attentions are paid to integral inequalities for discontinuous functions.In this paper,an estimation of unknown functions of a class of integral inequalities for discontinuous functions by techniques of analysis and mathematical induction is given.Using the result we can solve both the integral inequalities for discontinuous functions in literature（Nonlinear Anal,2007,66：498-508）.We apply the result to a class of differential equations with impulse perturbation to find out the upper bound.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2011年第1期43-46,共4页
Journal of Sichuan Normal University（Natural Science）
基金
广西自然科学基金(0991265)
广西教育厅科学研究项目(200707MS112)
广西教改项目(200710961)资助项目
关键词
非连续函数积分不等式
未知函数估计
脉冲微分方程
integral inequality for discontinuous function
estimation of unknown function
differential equation with impulse perturbation
