一类Volterra型积分方程组的正整体解的存在性

Global Existence of Positive Solutions for a Class of Volterra Integral Equations

本文考虑下面的Ｖｏｌｔｅｒｒａ型积分方程组的正整体解的存在性．证明了如果Ｉ－Ａ是正定矩阵，那么（Ｉ）存在整体正解；如果Ｉ－Ａ不是正定矩阵，那么（Ｉ）不存在连续不减正解，其中Ｉ是Ｎ阶单位矩阵，Ａ＝（ｍｉｊ）Ｎ．Ｎ，ｍｉｊ≥０，ａｉ＞０．

This paper considers the global existence and nonexistence of positive solutions for the following Volterra integral equations where . It is Proved that if I - A is a positive definite matrix,where I is an identity matrix, A = (mij)N. N, then (I) has global positive Solution; Otherwise, (I)has no continous nondecreasing positive solution.