Discrete Systems

Ravi P. Agarwal and Donal O’Regan
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Ravi P. Agarwal: National University of Singapore
Donal O’Regan: University of Ireland

Chapter Chapter 5 in Infinite Interval Problems for Differential, Difference and Integral Equations, 2001, pp 233-276 from Springer

Abstract: Abstract Let x : ℕ → ℝ n with x(k) = (x 1(k), ..., x n (k)). Consider the discrete system (5.1.1) $$ x(k + 1) = \sum\limits_{i = 0}^k {A_k (i)x(i) + b(k) + f_k (x(0),x(1), \ldots ,x(k)),k \in } \mathbb{N}$$ where each A k (i) is a constant n × n matrix, b(k) is an n-vector, and f k : ℝ n(k+1) → ℝ n with the dependence of f k at k annotated in the subscript.

Keywords: Difference Equation; Fixed Point Theorem; Discrete System; Discrete Topology; Lebesgue Dominate Convergence Theorem (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-94-010-0718-4_5

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