On the Kneser problem for two-dimensional differential systems with advanced arguments (Q701417)

Here, the authors consider the problem of finding a solution to the system \[ u_i'(t)= f_i(t,u_1(\tau_{i1}(t)), u_2(\tau_{i2}(t))),\quad i= 1,2, \] satisfying \[ \varphi(u_1(0), u_2(0))= 0,\quad u_1(t)\geq 0,\quad u_2(t)\geq 0\quad\text{for }t\geq 0. \] Sufficient conditions for the solvability of this problem are given.