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${𝒞}^{m}$-smoothness of invariant fiber bundles for dynamic equations on measure chains.

Advances in Difference Equations [electronic only]

A class of infinite series including terms of generalized sequences.

Boletín de la Asociación Matemática Venezolana

A Levy-Khinchin Formula for Semigroups with Involutions.

Mathematische Annalen

A proof of a conjecture by Karamata.

Publications de l'Institut Mathématique [Elektronische Ressource]

A proof of Leibniz's formula for divided differences.

General Mathematics

Addendum to the article: Polylogarithms in the field of omega (a root of a given cubic): Functional equations and ladders.

Aequationes mathematicae

An Apéry-like difference equation for Catalan's constant.

The Electronic Journal of Combinatorics [electronic only]

Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order

Serdica Mathematical Journal

Orthonormal polynomials on the real line {pn (λ)} n=0 ... ∞ satisfy the recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) = λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 = 0, λ ∈ C. In this paper we study systems of polynomials {pn (λ)} n=0 ... ∞ which satisfy the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) + αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R, n = 0, 1, 2, . . ., α−1 = α−2...

Asymptotical behaviors of nonautonomous discrete Kolmogorov system with time lags.

Advances in Difference Equations [electronic only]

Basic concepts of the difference geometry

Annales Polonici Mathematici

Characterization of a class of functions using divided differences.

Abstract and Applied Analysis

Conservation laws of discrete Korteweg-de Vries equation.

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Covering systems, Kubert identities and difference equations

Mathematica Slovaca

Acta Arithmetica

Distribution of zeros and shared values of difference operators

Annales Polonici Mathematici

We investigate the distribution of zeros and shared values of the difference operator on meromorphic functions. In particular, we show that if f is a transcendental meromorphic function of finite order with a small number of poles, c is a non-zero complex constant such that ${\Delta }_{c}^{k}f\ne 0$ for n ≥ 2, and a is a small function with respect to f, then $fⁿ{\Delta }_{c}^{k}f$ equals a (≠ 0,∞) at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved.

Ein Beitrag zur Differenzrechnung und zur Zahlentheorie.

Mathematische Annalen

Aktuárské vědy

Équations aux différences associées à des groupes, fonctions représentatives.

Annales de l’institut Fourier

Inspiré par un travail de J.-P. Bézivin et F. Gramain sur les systèmes d’équations aux différences, on caractérise les sous-groupes $H$ d’un groupe de Lie réel (resp. complexe) $G$, pour lesquels toute fonction $f:G\to ℂ$ continue (resp. entière) telle que l’ensemble des $H$-translatées engendrent un $ℂ$-espace vectoriel de dimension finie, engendrent aussi un $ℂ$-espace vectoriel de dimension finie par $G$- translation. On fait le lien avec les systèmes d’équations aux différences à coefficients constants.

Étude sur les équations fonctionnelles

Annales scientifiques de l'École Normale Supérieure

Existence and positivity of solutions for a nonlinear periodic differential equation

Archivum Mathematicum

We study the existence and positivity of solutions of a highly nonlinear periodic differential equation. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ a modification of Krasnoselskii’s fixed point theorem introduced by T. A. Burton ([4], Theorem 3) to show the existence and positivity of solutions of the equation.

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