Consider the following n-th
order nonlinear differential equation
(1)
All functions considered will be assumed continuous and au the solutions of (1),
continuously extendable throught the entire nonnegative real axis. A nontrivial
solution of (1) is called oscillatory if it has zeros for arbitrarily large t and equation
(1) is called oscillatory if all of its solutions are oscillatory. A nontrivial
solution of (1) is called nonoscillatory if it has only a finite number of zeros on
[t0,∞) and equation (1) is called nonoscillatory if all of its solutions are
nonoscillatory. In this paper, theorems on oscillation and nonoscillation are
presented.