Oscillation and asymptotic behavior of solutions of Nth order nonlinear delay differential equations

Oscillation and Asymptotic Behavior of Solutions of Nth Order Nonlinear Delay Differential Equations*

where n >, 2, a: [0, 00) + [0, a~), q: [0, co) --+ (-00, co), andf: (--co, 03) + (-00, CQ). We assume a(l), q(t), andf( x are continuous, q(t) < t for all t > 0, q(t) 3 co ) as t ---f co, and xf(x) > 0 for x # 0. Usually, a condition of monotonicity on f is needed in order to obtain results for Eq. (1) analogous to those of an ordinary differential equation of the same type. Many authors observ...

Oscillation and Asymptotic Behavior of Higher-Order Nonlinear Differential Equations

Oscillation and Asymptotic Behavior of Solutions of Certain Third-Order Nonlinear Delay Dynamic Equations

The paper deals with the oscillation and asymptotic behavior of solutions of the third-order nonlinear delay dynamic equation { b(t) ([ a(t) ( x(t) )α]∆ )β}∆ + f(t, x(τ(t))) = 0 on a time scale T, where α, β > 0 are quotients of odd positive integers. We obtain some sufficient conditions which ensure that every solution of the equation either oscillates or converges to zero. Our results extend ...

Oscillation properties of nonlinear neutral differential equations of nth order

We consider the nonlinear neutral functional differential equation [r (t)[x(t) + b a p(t, µ)x(τ(t, µ))dµ] (n−1) ] + δ d c q(t, ξ)f (x(σ (t, ξ)))dξ = 0 with continuous arguments. We will develop oscillatory and asymptotic properties of the solutions. have studied the oscillation theory of second-order and higher-order neutral functional differential equations, in which the highest-order derivati...

ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *

The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.