Page 1 Next

Displaying 1 – 20 of 65

Showing per page

A note on algebraic differential equations whose coefficients are entire functions of finite order

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

A result concerning meromorphic solutions in the unit disk of algebraic differential equations

Compositio Mathematica

Addendum to "On Meromorphic Solutions of Algebraic Differential Equations".

Commentarii mathematici Helvetici

Analytic solutions of a second-order functional differential equation with a state derivative dependent delay

Colloquium Mathematicae

This paper is concerned with a second-order functional differential equation of the form ${x}^{\text{'}\text{'}}\left(z\right)=x\left(az+b{x}^{\text{'}}\left(z\right)\right)$ with the distinctive feature that the argument of the unknown function depends on the state derivative. An existence theorem is established for analytic solutions and systematic methods for deriving explicit solutions are also given.

Anwendung der Methode von Šapkarev zum Auflosen Einige Randwertaufgaben für die Lineare Komplexe Differentialgleichung II Ordnung

Matematički Vesnik

Asymptotic estimates for the growth of meromorphic solutions to differential equations in angular domains.

Siberian Mathematical Journal

Bounded index, entire solutions of ordinary differential equations and summability methods.

International Journal of Mathematics and Mathematical Sciences

Consequences of the meromorphic equivalence of standard matrix differential equations.

Publicacions Matemàtiques

In this article we investigate the question [of] how meromorphic differential equations can be simplified by meromorphic equivalence. In the case of equations of block size 1, which generalizes the case of distinct eigenvalues, we identify a class of equations which are simplest possible in the sense that they carry the smallest number of parameters whithin their equivalence classes. We also discuss conditions under which individual equations can be simplified. Particular attention is paid to the...

Distributional and entire solutions of ordinary differential and functional differential equations.

International Journal of Mathematics and Mathematical Sciences

Double exponential estimate for the number of zeros of complete Abelian integrals and rational envelopes of linear ordinary differential equations with an irreducible monodromy group.

Inventiones mathematicae

Estimation of the hyper-order of entire solutions of complex linear ordinary differential equations whose coefficients are entire functions.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Existence and uniqueness of analytic solutions of the Shabat equation.

Abstract and Applied Analysis

Existence of meromorphic solutions of algebraic differential equations.

Mathematica Scandinavica

Explicit rational solutions of Knizhnik-Zamolodchikov equation

Open Mathematics

We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions generated by elements of the symmetric group ${𝒮}_{n}$ n. We assume that parameter ρ = ±1. In previous paper  we proved that the fundamental solution of the corresponding KZ-equation is rational. Now we construct this solution in the explicit form.

Floquet theory for linear differential equations with meromorphic solutions.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

General solution of overdamped Josephson junction equation in the case of phase-lock.

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

Generalized trigonometric functions in complex domain

Mathematica Bohemica

We study extension of $p$-trigonometric functions ${sin}_{p}$ and ${cos}_{p}$ to complex domain. For $p=4,6,8,\cdots$, the function ${sin}_{p}$ satisfies the initial value problem which is equivalent to (*) $-{\left({u}^{\text{'}}\right)}^{p-2}{u}^{\text{'}\text{'}}-{u}^{p-1}=0,\phantom{\rule{1.0em}{0ex}}u\left(0\right)=0,\phantom{\rule{1.0em}{0ex}}{u}^{\text{'}}\left(0\right)=1$ in $ℝ$. In our recent paper, Girg, Kotrla (2014), we showed that ${sin}_{p}\left(x\right)$ is a real analytic function for $p=4,6,8,\cdots$ on $\left(-{\pi }_{p}/2,{\pi }_{p}/2\right)$, where ${\pi }_{p}/2={\int }_{0}^{1}{\left(1-{s}^{p}\right)}^{-1/p}$. This allows us to extend ${sin}_{p}$ to complex domain by its Maclaurin series convergent on the disc $\left\{z\in ℂ:|z|<{\pi }_{p}/2\right\}$. The question is whether this extensions ${sin}_{p}\left(z\right)$ satisfies (*) in the sense of differential equations in complex domain. This interesting...

Growth and fixed points of meromorphic solutions of higher order linear differential equations

Annales Polonici Mathematici

We investigate the growth and fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives. Our results extend the previous results due to Peng and Chen.

Growth of solutions to higher order linear homogeneous differential equations in angular domains.

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

Page 1 Next