一类新型时滞积分不等式及其应用

主要研究了一种新型时滞积分不等式u(t)≤a(t)+∫0α(t)f(t,s)w(u(s))ds+∫0α(t)g(t,s∫)0sh(s,τ)φ(u(τ))dτds up(t)≤a(t)+p/p-q∫0α(t)(f(t,s)uq(s)w(u(s))+g(t,s)uq(s))dsup(t)≤a(t)+p/p-q∫0α(t)f(t,s)uq(s)w(u(s))ds+p/p-q∫0tg(t,s)uq(s)w(u(s))ds这里p>q≥0是常数且t∈[0,∞).并且用此结果研究了时滞微分积分方程解的全局存在性和有界性.

A Class of New Retarded Integral Inequlities and Their Application

We consider a class of new retarded integral inequalitiesu(t)≤a(t)+∫α(t)0f(t,s)w(u(s))ds+∫α(t)0g(t,s)∫s0h(s,τ)φ(u(τ))dτdsup(t)≤a(t)+p/p-q∫α(t)0(f(t,s)uq(s)w(u(s))+g(t,s)uq(s))dsup(t)≤a(t)+p/p-q∫α(t)0f(t,s)uq(s)w(u(s))ds+p/p-q∫t0g(t,s)uq(s)w(u(s))dswhere p>q≥0 are constants and t∈[0,∞). The results five here can be applied to the global existence and boundedness of solutions to differential equations with time delay.