Asymptotic properties of solutions of certain third-order dynamic equations

In this paper, the well known oscillation criteria due to Hille and Nehari for second-order linear differential equations will be generalized and extended to the third-order nonlinear dynamic equation

(r₂(t)((r₁(t)x^Δ(t))^Δ)^γ)^Δ+q(t)f(x(t))=0     

Global behavior of a higher order nonlinear difference equation

In this paper, we consider a higher order difference equation of the form

     

First order difference equations with maxima and nonlinear functional boundary value conditions

This paper is devoted to the existence of solutions for a problem of first order difference equations with maxima and with nonlinear functional boundary value conditions. Such boundary conditions include, among others, initial, periodic, antiperiodic and multipoint boundary value conditions, as particular cases.     

Oscillatory criteria for third-order nonlinear difference equation with impulses

In this paper, we study the oscillation of a third-order nonlinear difference equation with impulses. Some sufficient conditions for the oscillatory behavior of solutions of third-order impulsive nonlinear difference equation are obtained. Some known results in the literature are generalized and improved.     

The entire solutions of a polynomial difference equation

Recently S. Shimomura has shown that the polynomial difference equationw(z + 1) =P(w(z)), whereP is a given polynomial of degree at least two, always has entire non-constant solutions. The present investigation shows how to construct all entire solutions of the equation and discusses some properties of the solutions.     

Asymptotic behavior of solutions of a nonlinear difference equation with continuous argument

We consider the difference equation with continuous argument

Persistence of solutions to higher order nonlinear Schrödinger equation

Applying an Abstract Interpolation Lemma, we showed persistence of solutions of the initial value problem to higher order nonlinear Schrödinger equation, also called Airy-Schrödinger equation, in weighted Sobolev spaces X2,θ, for θ∈[0,1].     

Asymptotic behavior of solutions of A 2nth order nonlinear differential equation

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for

On the dynamics of a higher order rational difference equations

The main objective of this paper is to study the global stability of the positive solutions and the periodic character of the difference equation

$y_{n+1}=a{y}_n+b{y}_{n?t}+c{y}_{n?l}+\frac{d{y}_{n?k}+e{y}_{n?s}}{\alpha y_{n?k}+\beta y_{n?s}},n=0,1,\dots ,$

with positive parameters and non-negative initial conditions. Numerical examples to the difference equation are given to explain our results.     

Asymptotic behavior of a nonlinear delay difference equation

This paper considers a class of nonlinear difference equations

Δ₃y_n + ƒ(n, y_n, y_n−r) = 0, n N (n₀)

. A necessary and sufficient condition for the existence of a bounded nonoscillatory solution is given.     

Oscillatory criteria for Third-Order difference equation with impulses

In this paper, we investigate the oscillation of Third-order difference equation with impulses. Some sufficient conditions for the oscillatory behavior of the solutions of Third-order impulsive difference equations are obtained.