一类幂形式的非线性Volterra-Fredholm型积分不等式

摘要

本文研究了一类幂形式的非线性Volterra-Fredholm型积分不等式，u(t)≤k+ʃa(t)a(t0)σ1(s)[f(s)u½(s)+ʃsa(t0)σ2(ґ)u½(ґ)dґ]ds+ʃa(T)a(t0)σ1(s)[f(s)u½(s)+ʃsa(t0)σ2(ґ)u½(ґ)u½(ґ)dґ]ds,t∈[t0,T]的解估计。%This paper studies a class of nonlinear Volterra-Fredholm type integral inequality.u(t)≤k+ʃa(t)a(t0)σ1(s)[f(s)u½(s)+ʃsa(t0)σ2(ґ)u½(ґ)dґ]ds+ʃa(T)a(t0)σ1(s)[f(s)u½(s)+ʃsa(t0)σ2(ґ)u½(ґ)u½(ґ)dґ]ds,t∈[t0,T].We are given the estimate of unknown function of the inequality.