Abstract: This paper considers the global existence and nonexistence of positive solutions for the following volterra integral equations (I) ... Matrix B is called a positive definite one,if all the k-th(k=1,2,3 )principal minors have positive deteminants.By considering theexistence of  positivve solutions for algebra equations,it is proved that if I-A is a positive definite matrix, where  I  is  an  identity  matrix,A=(m;), then (I) has  global  positive  solution;Otherwise,(I) has no continous nondeereasing positive solution.

Key words: arwrds volterra , inegral , equations;globel , solution;positive , solution , of algebra , equation