Oscillation criteria for a linear neutral differential equation

Conditions for Oscillation of a Neutral Differential Equation

Oscillation for a second-order neutral differential equation with impulses

We consider a certain type of second-order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations (called impulses). As a matter of fact, some particular non-impulsive cases of the system are oscillatory already. Thus, we are interested in finding adequate impulse controls under which our...

Oscillation criteria for even-order neutral differential equations

Our aim in this paper is to present sufficient conditions for the oscillation of the second order neutral differential equation ( x(t)− px(t− τ ))′′ + q(t)x(σ(t)) = 0.

Oscillation criteria for second order nonlinear neutral differential equations

This paper is concerned with the oscillation of second-order nonlinear neutral differential equations of the form [ r(t)[(x(t) + p(t)x(σ(t)))′]γ ]′ + f(t, x(τ(t))) = 0, by using a generalized Riccati’s technique and integral averaging technique, we establish new oscillation results which handle some cases not covered by known criteria.

Oscillation criteria for first-order neutral differential equations

d Ž . Ž . Ž . Sufficient conditions for the oscillation of the equation x t R t x t r dt Ž . Ž . Ž . Ž . Ž . . Ž . P t x t Q t x t 0, where P, Q, R C t , , R , r 0, , 0 Ž . t Ž . , R , , are obtained where R t H Q u du 1 is allowed to t Ž . Ž . Ž . Ž oscillate and the condition H s P s Q s H P u Q u t s 0 . du ds is not necessary. Some examples are given, which show that the results here are al...