脉冲积分不等式未知函数的估计

Estimation of Unknown Function of Impulsive Integral Inequality

积分不等式是研究微分方程和积分方程的重要工具.对非连续函数积分不等式中未知函数进行估计,可以研究某些脉冲微分系统和脉冲积分系统解的一些重要性质.建立了一类新的积分不等式,其不等式左端为未知函数的非线性因子,右端和项中也为未知函数的非线性因子.利用数学归纳法给出了未知函数的上界估计,并用求得的结果给出了脉冲微分方程解的估计.

Integral inequality is an important tool in the study of differential and integral equations. To estimate the unknown function of integral inequalities for discontinuous functions, one can study the properties of solutions for some impulsive differential system and impulsive integral equations. In this paper, a class of new integral inequalities for discontinuous functions is established. The left side of the inequality is a nonlinear factor of unknown function, and the sum-term of the right side of the inequality for the unknown function is also a nonlinear factor. Using mathematical induction, an estimation of upper bound of the unknown function is obtained. Finally, the result is applied to give an estimation of the solutions of impulsive differential equations.