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A fixed point method to compute solvents of matrix polynomials

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

Compositio Mathematica

Acta Arithmetica

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

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$x\frac{d\stackrel{\to }{y}}{dx}={\stackrel{\to }{G}}_{0}\left(x\right)+\left[\lambda \left(x\right)+{A}_{0}\right]\stackrel{\to }{y}+{x}^{\mu }\stackrel{\to }{G}\left(x,\stackrel{\to }{y}\right),$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

Compositio Mathematica

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

Czechoslovak Mathematical Journal

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

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A reduction theory of second order meromorphic differential equations. II

Annales scientifiques de l'École Normale Supérieure

Additive groups connected with asymptotic stability of some differential equations

Archivum Mathematicum

The asymptotic behaviour of a Sturm-Liouville differential equation with coefficient ${\lambda }^{2}q\left(s\right),\phantom{\rule{4pt}{0ex}}s\in \left[{s}_{0},\infty \right)$ is investigated, where $\lambda \in ℝ$ and $q\left(s\right)$ is a nondecreasing step function tending to $\infty$ as $s\to \infty$. Let $S$ denote the set of those $\lambda$’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 $S=\left\{0\right\}$, $S=ℤ$, $S=𝔻$ (i.e. the set of dyadic numbers), and $ℚ\subset S⫋ℝ$.

Revista colombiana de matematicas

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

Rendiconti del Seminario Matematico della Università di Padova

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

Rendiconti del Seminario Matematico della Università di Padova

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

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.

Analytic First Integrals of Ordinary Differential Equations

Commentarii mathematici Helvetici

Applications de la théorie de Nevanlinna p-adique.

Collectanea Mathematica

Asymptotic behaviour of equations $\stackrel{˙}{z}=q\left(t,z\right)-p\left(t\right){z}^{2}$ and $\stackrel{¨}{x}=x\varphi \left(t,\stackrel{˙}{x}{x}^{-1}\right)$

Archivum Mathematicum

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

Archivum Mathematicum

Asymptotic behaviour of the system of two differential equations

Archivum Mathematicum

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

Archivum Mathematicum

Asymptotische Eigenschaften der Differentialgleichung ${y}^{\text{'}\text{'}}+2{a}_{1}\left(x\right){y}^{\text{'}}+{a}_{2}\left(x\right)y=0$

Czechoslovak Mathematical Journal

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