The bounded solutions to nonlinear fifth-order differential equations with delay

On the stability of solutions of nonlinear differential equations of fifth order with delay

Criteria for global asymptotic stability of a null solution of a nonlinear differential equation of fifth order with delay x(t) + ψ(x(t− r), x′(t− r), x′′(t− r), x′′′(t− r), x(t− r))x(t) +f(x′′(t− r), x′′′(t− r)) + α3x(t) + α4x(t) + α5x(t) = 0 are obtained by using Lyapunov’s second method. By defining a Lyapunov functional, sufficient conditions are established, which guarantee the null soluti...

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 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...

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...

On the Number of Zeros of Bounded Nonoscillatory Solutions to Higher-order Nonlinear Ordinary Differential Equations