Jjam Jan Brands

Oscillation theorems for second-order functional differential equations

Abstract This paper presents some comparison theorems on the oscillatory behavior of solutions of second-order functional differential equations. Here we state one of the main results in a simplified form: Let q, τ1, τ2 be nonnegative continuous functions on (0, ∞) such that τ1 − τ2 is a bounded function on [1, ∞) and t − τ1(t) → ∞ if t → ∞. Then y (t) + q(t) y(t − τ 1 (t)) = 0 is oscillatory if and only if y (t) + q(t) y(t − τ 2 (t)) = 0 is oscillatory.

Asymptotics of a nonlinear delay differential equation

Abstract Sufficient conditions will be given for the existence of the limit of f ( x ) for x →∞ if f is a solution of w ( x ) f ′( x ) = g ( f ( x − 1) − f ( x )).