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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 $ℚ\subset S⫋ℝ$.

### Algunas Propiedades De Regularidad De Las Ecuaciones Diferenciales Complejas.

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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