Nonlinear oscillations in disconjugate forced functional equations with deviating arguments.

Singh, Bhagat

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In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form $y_{i}^{'} (t) - p_{i} (t) y_{i + 1} (t) = 0, i = 1, 2, \dots, n - 2, y_{n - 1}^{'} (t) - p_{n - 1} (t) | y_{n} (h_{n} (t)) |^{α} s g n [y_{n} (h_{n} (t))] = 0, y_{n}^{'} (t) s g n [y_{1} (h_{1} (t))] + p_{n} (t) {| y_{1} (h_{1} (t)) |}^{β} \leq 0,$ where $n \geq 3$ is odd, $α > 0$ , $β > 0$ .