Oscillation of a system of two functional differential equations (Q1343468)

Sufficient conditions under which the first component of every solution to the system of two differential equations \(x_ i'(t) = f_ i [t, x_ 1 (g_{i1} (t,x_ 1(t), x_ 2(t))), x_ 2 (g_{i2} (t, x_ 1(t), x_ 2(t)))]\), \(i = 1,2\); \(t \in R_ +\); \(f_ i, g_{ij} \in C(R_ + \times R^ 2,R)\), \(i,j = 1,2\), is either identically equal to zero or oscillatory are established. Solution-dependent deviating arguments \(g_{ij}\) may be retarded or advanced or otherwise. Two cases are considered: the function \(x_ 1 \to f_ 2 (t, x_ 1, x_ 2)\) is \(1^ 0\) strongly superlinear and \(2^ 0\) strongly sublinear.