Eventually positive solutions of odd order neutral differential equations

Existence for Eventually Positive Solutions of High-Order Nonlinear Neutral Differential Equations with Distributed Delay

Oscillation of Solutions for Odd-order Neutral Functional Differential Equations

In this article, we establish oscillation criteria for all solutions to the neutral differential equations [x(t)± ax(t± h)± bx(t± g)] = p Z d

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 Positive Solutions of Neutral Differential Equations

and Applied Analysis 3 We now define two maps S1 and S2 : Ω → C t0,∞ , R as follows: S1x t ⎧⎨ ⎩ a t x t − τ , t ≥ t1, S1x t1 , t0 ≤ t ≤ t1, S2x t ⎪⎨ ⎪⎩ − 1 n − 1 ! ∫∞ t s − t n−1p s f x s − σ ds, t ≥ t1, S2x t1 v t − v t1 , t0 ≤ t ≤ t1. 2.5 We will show that for any x, y ∈ Ω we have S1x S2y ∈ Ω. For every x, y ∈ Ω and t ≥ t1 we obtain S1x t ( S2y ) t ≤ a t v t − τ − 1 n − 1 ! ∫∞ t s − t n−1p s ...

Existence of Positive Periodic Solutions for Neutral Functional Differential Equations

We find sufficient conditions for the existence of positive periodic solutions of two kinds of neutral differential equations. Using Krasnoselskii’s fixed-point theorem in cones, we obtain results that extend and improve previous results. These results are useful mostly when applied to neutral equations with delay in bio-mathematics.