Hajnalka Péics

Differential equations with several non-monotone arguments: An oscillation result

Abstract This paper is concerned with the oscillatory behavior of first-order differential equations with several non-monotone delay arguments and non-negative coefficients. A sufficient condition, involving lim sup , which guarantees the oscillation of all solutions is established. Also, an example illustrating the significance of the result is given.

On the asymptotic behaviour of a pantograph–type difference equation

In this paper we study the asymptotic behaviour of solutions of the pantograph-type differnce equation, and obtain aymptotic estimates, which can imply asymptotic stability or stability of solutions

Positive solutions of second-order linear difference equation with variable delays

AbstractIn this paper we consider the second-order linear difference equations with variable delays Δ2a(n)+∑i=1mPi(n)a(n−ki(n))=0,n≥n0, where n0,n∈N, N is the set of positive integers. Using the method of Riccati transform and the generalized characteristic equations, we give sufficient conditions for the existence of positive solutions.MSC:39A11, 39A12.

On the Asymptotic Behaviour of the Solutions of a System of Functional Equations

AbstractIn this paper we study the asymptotic behaviour of the solutions of the functional equation

Representation of solutions of difference equations with continuous time.

x(t) = A(t)x(t - 1) + B(t)x(p(t)),

Existence of positive solutions of halflinear delay differential equation

, where x(t) ∈ Rn, A and B are n × n real matrix valued functions, p is a real function with p(t) < t − δ for some δ > 0 and limt→∞p(t) = ∞. In the first part of the paper we obtain asymptotic estimates for the rate of convergence of the solutions in the case when A(t) is a diagonal matrix. In the second part we prove results without assuming that A(t) is diagonal.