Oscillatory solutions of a system of \(n\) nonlinear integro-differential equations of second order with deviating arguments (Q686841)

The paper deals with the system of integro-differential equations with deviating arguments (1) \(y_ i''(t)=\int_ 0^ tf_ i \bigl(t,s;y_ 1(s),\ldots,y_ n(s)\); \(y_ 1(g_ 1(s)), \ldots,y_ n(g_ n(s))\bigr)\) \((i=1,\ldots,n)\), where the functions \(f_ i:R^ +\times R^ +\times R^ n \times R^ n \to R\) \((i=1,\ldots,n)\) are continuous, the functions \(g_ k:R^ +\to R^ + (k=1, \ldots ,n)\) are continuous, non-drecreasing and such that \(g_ k(t)\leq t\) or \(g_ k(t)>t\) for all \(t\) and \(\lim_{t \to \infty}g_ k(t)=\infty\). The author establishes sufficient conditions under which every solution of the system (1) is oscillatory.