Małgorzata Migda

On a class of fourth-order nonlinear difference equations

We consider a class of fourth-order nonlinear difference equations. The classification of nonoscillatory solutions is given. Next, we divide the set of solutions of these equations into two types: F+- and F−-solutions. Relations between these types of solutions and their nonoscillatory behavior are obtained. Necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties.

Oscillatory and asymptotic properties of solutions of even order neutral difference equations

We study the neutral difference equation of the form Explicit sufficient conditions which guarantee that all solutions of the above equation are oscillatory are obtained.

Asymptotic properties of solutions of difference equations with several delays and Volterra summation equations

We study a scalar linear difference equation with several delays by transforming it to a system of Volterra equations without delays. The results obtained for this system are then used to establish oscillation criteria and asymptotic properties of solutions of the considered equation.

On the rational recursive sequence

Abstract In this paper we consider the difference equation (E) with positive parameters and nonnegative initial conditions. We use the explicit formula for the solutions of equation (E) in investigating their behavior.

Monotone Solutions of Neutral Difference Equations of Odd Order

A class of monotone sequences is introduced. A classification of all such monotone solutions of odd order neutral difference equation is established. Necessary and/or sufficient conditions are then derived for the existence of these solutions.

Convergence of solutions of higher order neutral difference equations with quasi-differences

Abstract A higher order nonlinear neutral difference equation with quasi-differences is studied. Sufficient conditions are established under which for every real constant there exists a solution of considered equation convergent to this constant.

Boundedness of solutions of difference systems with delays

We give sufficient conditions for the boundedness of all solutions of some classes of systems of difference equations with delays, by comparison of their norms with the solution of certain auxiliary scalar difference equations.

Asymptotic behavior of solutions of the m th-order nonhomogeneous difference equations

Abstract Asymptotic behavior of solutions of the mth-order difference equation of the form (E1) Δ m x n + ƒ(n, x n ,…, Δ m−1 x n ) = h n and some special case (E2) of these equation are investigated.

Bounded solutions of nonlinear discrete volterra equations

Abstract We give sufficient conditions, under which for every real constant, there exists a solution of the nonlinear discrete Volterra equation Δx(n)=b(n)+∑i=0nK(n,i)f(x(i)),