Implicit difference inequalities corresponding to first-order partial differential functional equations.
Inequalities among eigenvalues of second-order difference equations with general coupled boundary conditions.
Inequalities that lead to exponential stability and instability in delay difference equations.
Infinite horizon discrete time control problems for bounded processes.
Initial and boundary value problems for -th order difference equations
Initial data stability and admissibility of spaces for Itô linear difference equations
The admissibility of spaces for Itô functional difference equations is investigated by the method of modeling equations. The problem of space admissibility is closely connected with the initial data stability problem of solutions for Itô delay differential equations. For these equations the -stability of initial data solutions is studied as a special case of admissibility of spaces for the corresponding Itô functional difference equation. In most cases, this approach seems to be more constructive...
Initial-value problems for linear partial difference equations.
Instability of discrete systems.
Instanton-anti-instanton solutions of discrete Yang-Mills equations
We study a discrete model of the Yang-Mills equations on a combinatorial analog of . Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both the techniques of a double complex and the quaternionic approach.
Integrable discrete equations derived by similarity reduction of the extended discrete KP hierarchy.
Invariant foliations and stability in critical cases.
Inverse Limits, Economics, and Backward Dynamics.
We survey recent papers on the problem of backward dynamics in economics, providing along the way a glimpse at the economics perspective, a discussion of the economic models and mathematical tools involved, and a list of applicable literature in both mathematics and economics.
Iterated oscillation criteria for delay dynamic equations of first order.
Iterated oscillation criteria for delay partial difference equations
In this paper, by using an iterative scheme, we advance the main oscillation result of Zhang and Liu (1997). We not only extend this important result but also drop a superfluous condition even in the noniterated case. Moreover, we present some illustrative examples for which the previous results cannot deliver answers for the oscillation of solutions but with our new efficient test, we can give affirmative answers for the oscillatory behaviour of solutions. For a visual explanation of the examples,...
Jost solution and the spectrum of the discrete Dirac systems.
Kamenev type oscillation criteria for nonlinear difference equations
By means of Riccati transformation techniques, we establish some new oscillation criteria for second-order nonlinear difference equation which are sharp.
La filtration canonique par les pentes d’un module aux -différences et le gradué associé
Nous montrons que le polygone de Newton d’une équation aux -différences linéaire ne dépend que du module aux -différences correspondant. Nous interprétons les résultats classiques de factorisation convergente de Adams-Birkhoff-Guenther en termes d’existence d’une filtration canonique par les pentes. De plus, le gradué associé possède d’excellentes propriétés fonctorielles et tensorielles.
Large-time dynamics of discrete-time neural networks with McCulloch-Pitts nonlinearity.
Lieu des pôles d'un système holonome d'équations aux différences finies
Linear bifurcation analysis with applications to relative socio-spatial dynamics.