含多个非线性项的Gronwall-Bellman型非连续函数积分不等式的推广

Generalization of Gronwall-Bellman Type Integral Inequality of Discontinuous Functions with Multiple Nonlinear Terms

研究了含有未知函数的多个非线性项的非连续函数积分不等式,对每一个区间的估计,在未把不等式右边第一项放大为常数,而是保持为函数的情况下,利用分析技巧给出了未知函数的上界估计.利用此结果估计了脉冲微分方程解的上界.

In this paper,I give the upper bounds estimation of the unknown function contained in multiple nonlinear terms of integral inequality for discontinuous functions. I estimate each interval without enlarging the inequality of the first term on the right side to a constant,and remaining the case for a function. The result is used to estimate the upper bounds of impulsive differential equations.