Nonoscillatory Solutions to Second-Order Neutral Difference Equations

Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales

Bounded Nonoscillatory Solutions for First Order Neutral Delay Differential Equations

This paper deals with the first order neutral delay differential equation (x(t) + a(t)x(t− τ))′ + p(t)f(x(t− α)) +q(t)g(x(t − β)) = 0, t ≥ t0, Using the Banach fixed point theorem, we show the existence of a bounded nonoscillatory positive solution for the equation. Three nontrivial examples are given to illustrate our results. Mathematics Subject Classification: 34K4

Classification of Nonoscillatory Solutions of Higher Order Neutral Type Difference Equations

The authors consider the diierence equation () m yn ? pny n?k ] + qny (n+m?1) = 0 f(n)g is a sequence of integers with (n) n and limn!1 (n) = 1. They obtain results on the classiication of the set of nonoscillatory solutions of () and use a xed point method to show the existence of solutions having certain types of asymptotic behavior. Examples illustrating the results are included.

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...

Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions

The continuability, boundedness, monotonicity, and asymptotic properties of nonoscillatory solutions for a class of second-order nonlinear differential equations p t h x t f x′ t ′ q t g x t are discussed without monotonicity assumption for function g. It is proved that all solutions can be extended to infinity, are eventually monotonic, and can be classified into disjoint classes that are full...