Asymptotic Nature of Nonoscillatory Solutions of n th Order Retarded Differential Equations
Bhagat Singh · SIAM Journal on Mathematical Analysis · 1975
The equation $r(t)y^{(n)} (t) + r'(t)y^{(n - 1)} (t) + a(t)y_\tau (t) = f(t)$ is studied for its nonoscillation behavior. Under certain conditions, it is shown that if $y(t)$ is a nonoscillatory solution, then $y^{(n - 2)} (t) \to 0$ as $t \to \infty $. The theorem is then applied to the case of 2nd order and 3rd order equations.