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La filtration canonique par les pentes d’un module aux $q$ -différences et le gradué associé

Jacques Sauloy (2004)

Annales de l’institut Fourier

Nous montrons que le polygone de Newton d’une équation aux $q$ -différences linéaire ne dépend que du module aux $q$ -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.

Dai, Binxiang, Huang, Lihong, Qian, Xiangzhen (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Lieu des pôles d'un système holonome d'équations aux différences finies

Claude Sabbah (1992)

Bulletin de la Société Mathématique de France

Linear bifurcation analysis with applications to relative socio-spatial dynamics.

Sonis, M. (1997)

Discrete Dynamics in Nature and Society

Linear impulsive periodic system with time-varying generating operators on Banach space.

Wang, Jinrong, Xiang, X., Wei, W. (2007)

Advances in Difference Equations [electronic only]

Lineare Differenzengleichungen in mehreren Variablen.

Edmund Hlawka (1983)

Journal für die reine und angewandte Mathematik

Linearized Oscillation of Nonlinear Difference Equations with Advanced Arguments

Özkan Öcalan (2009)

Archivum Mathematicum

This paper is concerned with the nonlinear advanced difference equation with constant coefficients $x_{n + 1} - x_{n} + \sum_{i = 1}^{m} p_{i} f_{i} (x_{n - k_{i}}) = 0, n = 0, 1, \dots$ where $p_{i} \in (- \infty, 0)$ and $k_{i} \in {\dots, - 2, - 1}$ for $i = 1, 2, \dots, m$ . We obtain sufficient conditions and also necessary and sufficient conditions for the oscillation of all solutions of the difference equation above by comparing with the associated linearized difference equation. Furthermore, oscillation criteria are established for the nonlinear advanced difference equation with variable coefficients $x_{n + 1} - x_{n} + \sum_{i = 1}^{m} p_{i n} f_{i} (x_{n - k_{i}}) = 0, n = 0, 1, \dots$ where $p_{i n} \leq 0$ and $k_{i} \in {\dots, - 2, - 1}$ for $i = 1, 2, \dots, m$ .