O istnieniu i ograniczoności rozwiązań pewnego układu równań różniczkowo-całkowych z opóżnionym argumentem

Abstract

Under the assumptions 1°—7° (pages 25-26) it is proved, by Tonelli’s method, that the Cauchy problem for the system o f differential equations with delayed argument o f form ( 1), has at least one solution. If, furthermore, assumptions 1°—4° (page 28) are fulfilled, then each solution <Pv{t), v = 1 , 2 , . . . , « , of system (1) is bounded in the interval {A , B) and the limits t lim|ipv(0- jVv(r)*|,J’ =1 , 2 , ...,n, t - B A exist. These theorems generalize author’s results [3].