Asymptotic Properties of the Nonoscillatory Solutions of Second-Order Neutral Equations with a Deviating Argument

Oscillation of second order neutral equations with distributed deviating argument

Oscillation criteria are established for the second order neutral delay differential equation with distributed deviating argument (r(t) (x(t))Z′(t))′ + ∫ b a q(t, )f [x(g(t, ))] d ( )= 0, t t0, where Z(t)= x(t)+p(t)x(t − ). These results are extensions of the integral averaging techniques due to Coles and Kamenev, and improve some known oscillation criteria in the existing literature. © 2006 El...

On the Growth of Nonoscillatory Solutions for Difference Equations with Deviating Argument

The half-linear difference equations with the deviating argument Δ an|Δxn| sgn Δxn bn|xn q| sgn xn q 0 , q ∈ Z are considered. We study the role of the deviating argument q, especially as regards the growth of the nonoscillatory solutions and the oscillation. Moreover, the problem of the existence of the intermediate solutions is completely resolved for the classical half-linear equation q 1 . ...

Oscillation criteria for second-order neutral equations with distributed deviating argument

Nonoscillatory Solutions of Second Order Differential Equations with Integrable Coefficients

The asymptotic behavior of nonoscillatory solutions of the equation x" + a{t)\x\' sgnx = 0, y > 0 , is discussed under the condition that A(t) = limr_00/, a(s)ds exists and A(t) > 0 for all t. For the sublinear case of 0 < y < 1 , the existence of at least one nonoscillatory solution is completely characterized.

Existence of Nonoscillatory Bounded Solutions for a System of Second-order Nonlinear Neutral Delay Differential Equations

A system of second-order nonlinear neutral delay differential equations ( r1(t) ( x1(t) + P1(t)x1(t− τ1) )′)′ = F1 ( t, x2(t− σ1), x2(t− σ2) ) , ( r2(t) ( x2(t) + P2(t)x2(t− τ2) )′)′ = F2 ( t, x1(t− σ1), x1(t− σ2) ) , where τi > 0, σ1, σ2 ≥ 0, ri ∈ C([t0,+∞),R), Pi(t) ∈ C([t0,+∞),R), Fi ∈ C([t0,+∞)× R2,R), i = 1, 2 is studied in this paper, and some sufficient conditions for existence of nonosc...