Stability properties and asymptotic almost periodicity for linear Volterra difference equations in a Banach space

Uniform Asymptotic Stability and Robust Stability for Positive Linear Volterra Difference Equations in Banach Lattices

A dynamical system is called positive if any solution of the system starting from nonnegative states maintains nonnegative states forever. In many applications where variables represent nonnegative quantities we often encounter positive dynamical systems as mathematical models see 1, 2 , and many researches for positive systems have been done actively; for recent developments see, for example, ...

Strong Stability and Asymptotical Almost Periodicity of Volterra Equations in Banach Spaces

Stability properties and existence theorems of pseudo almost periodic solutions of linear Volterra difference equations

Correspondence: [email protected]. ac.jp Department of Information Science, Okayama University of Science, 1-1 Ridai-chyo, Kitaku, Okayama 700-0005, Japan Abstract The purpose of this article is to discuss the existence of pseudo almost periodic solutions of linear Volterra equation: x(n + 1) = A(n)x(n) + ∑n s=−∞ F(n, s)x(s) + p(n) , n Î Z, by using an exponentially stable of the zero solution, wh...

Asymptotic Properties for Half-linear Difference Equations

Dedicated to Prof. Jaroslav Kurzweil on the occasion of his 80th birthday Abstract. Asymptotic properties of the half-linear difference equation (∗) ∆(an|∆xn| α sgn∆xn) = bn|xn+1| α sgnxn+1 are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to (∗) are considered too. Our approach is based on a classification of solutions of (...

Asymptotic Representation of the Solutions of Linear Volterra Difference Equations

This article analyses the asymptotic behaviour of solutions of linear Volterra difference equations. Some sufficient conditions are presented under which the solutions to a general linear equation converge to limits, which are given by a limit formula. This result is then used to obtain the exact asymptotic representation of the solutions of a class of convolution scalar difference equations, w...