A Regularity Theorem for Certain 2nth-Order Nonlinear Differential Operator with a Parameter

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

Oscillation criteria for certain fourth order nonlinear functional differential equations

Some new criteria for the oscillation of the fourth order functional differential equation d dt ( 1 a3(t) ( d dt 1 a2(t) ( d dt 1 a1(t) ( d dt x(t) )α1)α2)α3) + δq(t) f (x[g(t)]) = 0, where δ = ±1 are established. c © 2006 Elsevier Ltd. All rights reserved.

Oscillation Theorems for Certain Higher Order Nonlinear Functional Differential Equations

Some new oscillation theorems for higher-order nonlinear functional differential equations of the form d n dt n a(t) d n x(t) dt n α + q(t)f x g(t) = 0, α > 0, are established.

Instability Results for Certain Third Order Nonlinear Vector Differential Equations

Our goal in this paper is to obtain sufficient conditions for instability of the zero solution to the non-linear vector differential equation ... X + F (X, Ẋ)Ẍ + G(Ẋ) + H(X) = 0. An example illustrates the results obtained.