含多重积分的Volterra型积分方程

A Volterra Type Iegral Equation Containing Multiple Integrals

考虑有序拓扑空间上含多重积分的Ｖｏｌｔｅｒｒａ型积分方程，给出了该方程具有一个可表为Ｎｅｕｍａｎｎ级数的Ｌ￣Ｐ解的充分条件，作为主要结果的应用，导出了一个一般的Ｖｏｌｔｅｒｒａ型积分不等式．

A Volterra type integral equation containing multiple integrals over an ordered topoiogi-cal space is studied.Sumcient conditions are given to ensure that there is a Lp solution ex-pressed as a Neumann series for such an equation.As an application of the result,an inte-gral inequality of ordinary Volterra type is derived.