Existence of Nonoscillation Solutions of Second-order Neutral Dierential Equations

Existence of positive solutions of higher-order nonlinear neutral equations

where n ≥  is an integer, τ > , σ ≥ , d > c ≥ , b > a ≥ , r, P ∈ C([t,∞), (,∞)), P ∈ C([t,∞)× [a,b], (,∞)), Q ∈ C([t,∞), (,∞)), Q ∈ C([t,∞)× [c,d], (,∞)), f ∈ C(R,R), f is a nondecreasing function with xf (x) > , x = . The motivation for the present work was the recent work of Culáková et al. [] in which the second-order neutral nonlinear differential equation of the form [ ...

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...

Existence of Positive Solutions of Second Order Neutral Dynamic Equations on Time Scales

In this paper, a class of second order neutral dynamic equations on time scales is studied. Various types of eventually positive solutions are given and the existence of these eventually positive solutions are then derived by means of Kranoselskii’s fixed point theorem. AMS subject classification: 34K25, 34K40.

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

Nonoscillation Criteria for Solutions of Higher-order Functional Difference Equations of Neutral Type

In this paper, we find necessary conditions for every solution of the neutral functional difference equation ∆m−1 ( rn∆(yn − pnyτ(n)) ) + qnG(yσ(n)) = fn to oscillate or to tend to zero as n→∞, where ∆ is the forward difference operator, given by ∆xn = xn+1−xn; and pn, qn, rn are sequences of real numbers with qn ≥ 0, rn > 0. It is supposed that τ(n) and σ(n) are increasing sequences of integer...