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On the rational recursive sequence x n + 1 = α 0 x n + α 1 x n - l + α 2 x n - k β 0 x n + β 1 x n - l + β 2 x n - k

E. M. E. Zayed, M. A. El-Moneam (2010)

Mathematica Bohemica

The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation x n + 1 = α 0 x n + α 1 x n - l + α 2 x n - k β 0 x n + β 1 x n - l + β 2 x n - k , n = 0 , 1 , 2 , ⋯ where the coefficients α i , β i ∈ ( 0 , ∞ ) for i = 0 , 1 , 2 , and l , k are positive integers. The initial conditions x - k , ⋯ , x - l , ⋯ , x - 1 , x 0 are arbitrary positive real numbers such that l < k . Some numerical experiments are presented.

Properties of solutions of quaternionic Riccati equations

Gevorg Avagovich Grigorian (2022)

Archivum Mathematicum

In this paper we study properties of regular solutions of quaternionic Riccati equations. The obtained results we use for study of the asymptotic behavior of solutions of two first-order linear quaternionic ordinary differential equations.

The inverse carrier problem

Grant B. Gustafson, Miroslav Laitoch (2002)

Czechoslovak Mathematical Journal

The problem was motivated by Borůvka’s definitions of the carrier and the associated carrier. The inverse carrier problem is precisely defined and partially solved. Examples are given.

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