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A fixed point method to compute solvents of matrix polynomials

Fernando Marcos, Edgar Pereira (2010)

Mathematica Bohemica

Matrix polynomials play an important role in the theory of matrix differential equations. We develop a fixed point method to compute solutions of matrix polynomials equations, where the matricial elements of the matrix polynomial are considered separately as complex polynomials. Numerical examples illustrate the method presented.

A general theorem concerning the growth of solutions of first-order algebraic differential equations

Steven B. Bank (1972)

Compositio Mathematica

A method in diophantine approximation V

Charles Osgood (1973)

Acta Arithmetica

A new proof of multisummability of formal solutions of non linear meromorphic differential equations

Jean-Pierre Ramis, Yasutaka Sibuya (1994)

Annales de l'institut Fourier

We give a new proof of multisummability of formal power series solutions of a non linear meromorphic differential equation. We use the recent Malgrange-Ramis definition of multisummability. The first proof of the main result is due to B. Braaksma. Our method of proof is very different: Braaksma used Écalle definition of multisummability and Laplace transform. Starting from a preliminary normal form of the differential equation $x \frac{d \vec{y}}{d x} = {\vec{G}}_{0} (x) + [λ (x) + A_{0}] \vec{y} + x^{μ} \vec{G} (x, \vec{y}),$ the idea of our proof is to interpret a formal power series solution...

A note on a theorem of C. L. Siegel concerning Bessel's equation

Steven B. Bank (1982)

Compositio Mathematica

A note on the oscillation of solutions of periodic linear differential equations

Steven B. Bank (1994)

Czechoslovak Mathematical Journal

A phase of the differential equation $y^{'} = Q (t) y$ with a complex coefficient $Q$ of the real variable

Staněk, Svatoslav (1986)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A reduction theory of second order meromorphic differential equations. II

W. B. Jurkat, H. J. Zwiesler (1988)

Annales scientifiques de l'École Normale Supérieure

Additive groups connected with asymptotic stability of some differential equations

Árpád Elbert (1998)

Archivum Mathematicum

The asymptotic behaviour of a Sturm-Liouville differential equation with coefficient $λ^{2} q (s), s \in [s_{0}, \infty)$ is investigated, where $λ \in ℝ$ and $q (s)$ is a nondecreasing step function tending to $\infty$ as $s \to \infty$ . Let $S$ denote the set of those $λ$ ’s for which the corresponding differential equation has a solution not tending to 0. It is proved that $S$ is an additive group. Four examples are given with $S = {0}$ , $S = ℤ$ , $S = 𝔻$ (i.e. the set of dyadic numbers), and $ℚ \subset S ⫋ ℝ$ .

Algunas Propiedades De Regularidad De Las Ecuaciones Diferenciales Complejas.

Jaime Rodriguez Montes (1980)

Revista colombiana de matematicas

An existence theorem for certain solutions of algebraic differential equations in sectors

Steven B. Bank (1974)

Rendiconti del Seminario Matematico della Università di Padova

An existence theorem for solutions of $n$ -th order nonlinear differential equations in the complex domain

Charles Powder (1979)

Rendiconti del Seminario Matematico della Università di Padova

An extension of the Newton-Puiseux polygon construction to give solutions of Pfaffian forms

José Cano (1993)

Annales de l'institut Fourier

We give a proof of the fact that any holomorphic Pfaffian form in two variables has a convergent integral curve. The proof gives an effective method to construct the solution, and we extend it to get a Gevrey type solution for a Gevrey form.

Currently displaying 1 – 20 of 180

Page 1 Next

Displaying 1 – 20 of 180

A fixed point method to compute solvents of matrix polynomials

A general theorem concerning the growth of solutions of first-order algebraic differential equations

A method in diophantine approximation V

A new proof of multisummability of formal solutions of non linear meromorphic differential equations

A note on a theorem of C. L. Siegel concerning Bessel's equation

A note on the oscillation of solutions of periodic linear differential equations

A phase of the differential equation $y^{'} = Q (t) y$ with a complex coefficient $Q$ of the real variable

A reduction theory of second order meromorphic differential equations. II

Additive groups connected with asymptotic stability of some differential equations

Algunas Propiedades De Regularidad De Las Ecuaciones Diferenciales Complejas.

An existence theorem for certain solutions of algebraic differential equations in sectors

An existence theorem for solutions of $n$ -th order nonlinear differential equations in the complex domain

An extension of the Newton-Puiseux polygon construction to give solutions of Pfaffian forms

Analytic First Integrals of Ordinary Differential Equations

Applications de la théorie de Nevanlinna p-adique.

Asymptotic behaviour of equations $\dot{z} = q (t, z) - p (t) z^{2}$ and $\ddot{x} = x ϕ (t, \dot{x} x^{- 1})$

Asymptotic behaviour of the equation $x^{''} + p (t) x^{'} + q (t) x = 0$ with complex-valued coefficients

Asymptotic behaviour of the system of two differential equations

Asymptotic nature of solutions of the equation $\dot{z} = f (t, z)$ with a complex valued function $f$

Asymptotische Eigenschaften der Differentialgleichung $y^{''} + 2 a_{1} (x) y^{'} + a_{2} (x) y = 0$

Currently displaying 1 – 20 of 180