Add to ORKGWe study the higher order difference equations of the following form mxn = an f(xσ(n) ) + bn. We are interested in the asymptotic behavior of solutions x of the above equation. Assuming f is a power type function and ∆ myn = bn, we present sufficient conditions that guarantee the existence of a solution x such that xn = yn + o(n s where s ≤ 0 is fixed. We establish also conditions under which for a given solution x there exists a sequence y such that ∆ myn = bn and x has the above asymptotic behavior
summary:The authors consider the difference equation \[ \Delta ^{m} [y_{n} - p_{n} y_{n - k}] + \del...
AbstractIt is known that if ∑∞j |pj| < ∞ then the Emden-Fowler difference equation (A) Δ2yn−1 = pnyγ...
AbstractWe prove that the Putnam difference equation xn+1=xn+xn−1+xn−2xn−3xnxn−1+xn−2+xn−3,n=0,1,… h...
summary:Asymptotic properties of solutions of the difference equation of the form \[ \Delta ^m x_n=a...
summary:The nonlinear difference equation \[ x_{n+1}-x_n=a_n\varphi _n(x_{\sigma (n)})+b_n, \qquad \...
summary:Using the method of variation of constants, discrete inequalities and Tychonoff’s fixed-poin...
summary:Asymptotic properties of solutions of difference equation of the form \[ \Delta ^m x_n=a_n\v...
This paper is concerned with the oscillation and asymptotic behaviour of nonoscillatory solutions of...
summary:The asymptotic and oscillatory behavior of solutions of mth order damped nonlinear differenc...
AbstractIn this paper, we consider a higher order difference equation of the form xn+1=f(xn,xn−k),n=...
AbstractThe aim of this note is to show that the following difference equation:xn+1=α+xn−k∑i=0k−1cix...
AbstractAn asymptotic formula, having bounded relative error, is developed for the numerical sequenc...
AbstractWe obtain asymptotic forms of positive solutions of third-order Emden–Fowler equations. Thes...
Abstract. Asymptotic properties of solutions of difference equation of the form ∆mxn = anϕn(xσ(n)) +...
Asymptotic and oscillatory behaviour of solutions of some class nonlinear difference equations is st...
summary:The authors consider the difference equation \[ \Delta ^{m} [y_{n} - p_{n} y_{n - k}] + \del...
AbstractIt is known that if ∑∞j |pj| < ∞ then the Emden-Fowler difference equation (A) Δ2yn−1 = pnyγ...
AbstractWe prove that the Putnam difference equation xn+1=xn+xn−1+xn−2xn−3xnxn−1+xn−2+xn−3,n=0,1,… h...
summary:Asymptotic properties of solutions of the difference equation of the form \[ \Delta ^m x_n=a...
summary:The nonlinear difference equation \[ x_{n+1}-x_n=a_n\varphi _n(x_{\sigma (n)})+b_n, \qquad \...
summary:Using the method of variation of constants, discrete inequalities and Tychonoff’s fixed-poin...
summary:Asymptotic properties of solutions of difference equation of the form \[ \Delta ^m x_n=a_n\v...
This paper is concerned with the oscillation and asymptotic behaviour of nonoscillatory solutions of...
summary:The asymptotic and oscillatory behavior of solutions of mth order damped nonlinear differenc...
AbstractIn this paper, we consider a higher order difference equation of the form xn+1=f(xn,xn−k),n=...
AbstractThe aim of this note is to show that the following difference equation:xn+1=α+xn−k∑i=0k−1cix...
AbstractAn asymptotic formula, having bounded relative error, is developed for the numerical sequenc...
AbstractWe obtain asymptotic forms of positive solutions of third-order Emden–Fowler equations. Thes...
Abstract. Asymptotic properties of solutions of difference equation of the form ∆mxn = anϕn(xσ(n)) +...
Asymptotic and oscillatory behaviour of solutions of some class nonlinear difference equations is st...
summary:The authors consider the difference equation \[ \Delta ^{m} [y_{n} - p_{n} y_{n - k}] + \del...
AbstractIt is known that if ∑∞j |pj| < ∞ then the Emden-Fowler difference equation (A) Δ2yn−1 = pnyγ...
AbstractWe prove that the Putnam difference equation xn+1=xn+xn−1+xn−2xn−3xnxn−1+xn−2+xn−3,n=0,1,… h...