On the Oscillation of Certain Third-order Difference Equations

Nonlinear oscillation of certain third-order neutral differential equation with distributed delay

The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...

On the Oscillatory Behavior for a Certain Class of Third Order Nonlinear Delay Difference Equations

By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria for a certain class of third order nonlinear delay difference equations. Our results extend and improve some previously obtained ones. An example is worked out to demonstrate the validity of the proposed results.

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

Oscillation Criteria for Certain Third Order Nonlinear Difference Equations

Some new criteria for the oscillation of all solutions of third order nonlinear difference equations of the form ∆ a(n)(∆ 2 x(n)) α + q(n)f (x[g(n)]) = 0 and ∆ a(n)(∆ 2 x(n)) α = q(n)f (x[g(n)]) + p(n)h(x[σ(n)]) with ∞ a −1/α (n) < ∞ are established.

PERIODIC SOLUTIONS OF CERTAIN THREE DIMENSIONAL AUTONOMOUS SYSTEMS

There has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. The popular Poincare-Bendixon theorem applies well to the former but not the latter (see [2] and [3]). We give a necessary condition for the existence of periodic solutions for the third order autonomous system...

Oscillation theorems for certain third order nonlinear delay dynamic equations on time scales

In this paper, we establish some new oscillation criteria for the third order nonlinear delay dynamic equations