Journal of Inequalities and Applications 
Volume 7 (2002), Issue 4, Pages 453-477
doi:10.1155/S1025583402000231

On the Kneser problem for two-dimensional differential systems with advanced arguments

I. Kiguradze and N. Partsvania

 A. Razmadze Mathematical Institute of the Georgian Academy of Sciences, Tbilisi, Georgia
Received 20 July 2000; Revised 7 November 2000

Abstract

For the differential system u′i(t)=fi(t,u1(τi1(t)),u2(τi2(t))) (i=1,2) with advanced arguments τik(i,k=1,2), sufficient conditions are established for the existence and uniqueness of a solution of the Kneser problem φ(u1(0),u2(0))=0,  u1(t)≥0,u2(t)≥0   for t≥0, and the asymptotic behaviour of this solution is studied.