非线性脉冲Volterra-Fredholm积分微分方程
On the Nonlinear Impulsive Volterra-Fredholm Integrodifferential Equations
摘要：
本文研究非线性Volterra-Fredholm脉冲积分微分方程解的存在唯一性.利用Picard算子理论，我们研究了积分微分方程中解对初始条件和非线性函数的数据依赖性。进一步，我们将分段连续函数的积分不等式推广到混合情形，并应用它通过$ε$ -近似解研究解对初值的依赖性.通过积分不等式得到的唯一性和相关性结果比Picard算子理论对方程中函数的限制要少。
英文摘要：
In this paper, we investigate existence and uniqueness of solutions of nonlinear Volterra-Fredholm impulsive integrodifferential equations. Utilizing theory of Picard operators we examine data dependence of solutions on initial conditions and on nonlinear functions involved in integrodifferential equations. Further, we extend the integral inequality for piece-wise continuous functions to mixed case and apply it to investigate the dependence of solution on initial data through $ε$-approximate solutions. It is seen that the uniqueness and dependency results got by means of integral inequity requires less restrictions on the functions involved in the equations than that required through Picard operators theory.
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