Eventually positive and bounded solutions of even-order nonlinear neutral differential equations

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

Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation

In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...

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

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...