一类非线性Volterra积分不等式

摘要

本文简要讨论Gronwall不等式的研究进展,并给出关于如下的一类非线性Volterra积分不等式的一个结果:w(u(t))≤g(t)+n∑i=1√ai(t)ai(t0)fi(t,s)mПj=1H(u(s))Gij(maxs-h≤ζ≤su(ζ))ds.%In this paper,we briefly review the development of research on Gronwall's inequality,then obtain a result for the following nonlinear Volterra-type integral inequality:w(u(t))≤g(t)+n∑i=1√ai(t)ai(t0)fi(t,s) mПj=1H(u(s）)Gij（maxs-h≤ζ≤su(ζ)）ds.