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### Anharmonic oscillators with infinitely many real eigenvalues and $\mathrm{𝒫𝒯}$-symmetry.

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

### Asymptotic analysis and special values of generalised multiple zeta functions

Banach Center Publications

This is an expository article, based on the talk with the same title, given at the 2011 FASDE II Conference in Będlewo, Poland. In the introduction we define Multiple Zeta Values and certain historical remarks are given. Then we present several results on Multiple Zeta Values and, in particular, we introduce certain meromorphic differential equations associated to their generating function. Finally, we make some conclusive remarks on generalisations of Multiple Zeta Values as well as the meromorphic...

### Complex Oscillation of Differential Polynomials Generated by Meromorphic Solutions of Linear Differential Equations

Publications de l'Institut Mathématique

### Convergence of formal solutions of first order singular partial differential equations of nilpotent type

Banach Center Publications

Let (x,y,z) ∈ ℂ³. In this paper we shall study the solvability of singular first order partial differential equations of nilpotent type by the following typical example: $Pu\left(x,y,z\right):=\left(y{\partial }_{x}-z{\partial }_{y}\right)u\left(x,y,z\right)=f\left(x,y,z\right){\in }_{x,y,z}$, where $P=y{\partial }_{x}-z{\partial }_{y}{:}_{x,y,z}{\to }_{x,y,z}$. For this equation, our aim is to characterize the solvability on ${}_{x,y,z}$ by using the Im P, Coker P and Ker P, and we give the exact forms of these sets.

### Euler's integral transformation for systems of linear differential equations with irregular singularities

Banach Center Publications

Dettweiler and Reiter formulated Euler's integral transformation for Fuchsian systems of differential equations and applied it to a definition of the middle convolution. In this paper, we formulate Euler's integral transformation for systems of linear differential equations with irregular singularities. We show by an example that the confluence of singularities is compatible with Euler's integral transformation.

### 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 and oscillation of differential polynomials in the unit disc.

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

### Growth and oscillation of some class of differential polynomials in the unit disc

Kragujevac Journal of Mathematics

### Growth and oscillation theory of solutions of some linear differential equations

Matematički Vesnik

### Growth of meromorphic solutions of higher-order linear differential equations.

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

### Growth of solutions of higher-order linear differential equations.

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

### Iterated order of solutions of linear differential equations with entire coefficients.

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

### Matrices de Stokes-Ramis et constantes de connexion pour les systèmes différentiels linéaires de niveau unique

Annales de la faculté des sciences de Toulouse Mathématiques

Etant donné un système différentiel linéaire de niveau unique quelconque, nous explicitons des formules donnant les multiplicateurs de Stokes en fonction de constantes de connexion dans le plan de Borel, généralisant ainsi les formules obtenues dans l’article Resurgence, Stokes phenomenon and alien derivatives for level-one linear differential systems (M. Loday-Richaud, P. Remy). Pour ce faire, nous nous ramenons à un système de niveaux $\le 1$ par la méthode classique de réduction du rang ; puis, nous...

### On subnormal solutions of periodic differential equations.

Abstract and Applied Analysis

### On the growth of solutions of some higher order linear differential equations

Applications of Mathematics

In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation $\begin{array}{cc}& {f}^{\left(k\right)}+{A}_{k-1}{f}^{\left(k-1\right)}+\cdots +{A}_{2}{f}^{\text{'}\text{'}}+\left({D}_{1}\left(z\right)+{A}_{1}\left(z\right){\mathrm{e}}^{az}\right){f}^{\text{'}}\hfill \\ & +\left({D}_{0}\left(z\right)+{A}_{0}\left(z\right){\mathrm{e}}^{bz}\right)f=F\phantom{\rule{1.0em}{0ex}}\left(k\ge 2\right),\hfill \end{array}$ where $a$, $b$ are complex constants that satisfy $ab\left(a-b\right)\ne 0$ and ${A}_{j}\left(z\right)$$\left(j=0,1...$

### On the hyper order of solutions of a class of higher order linear differential equations.

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

### Oscillation of fast growing solutions of linear differential equations in the unit disc.

Acta Universitatis Sapientiae. Mathematica

### Oscillation of solutions of some higher order linear differential equations.

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

### Oscillation results on meromorphic solutions of second order differential equations in the complex plane.

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

### Quasialgebraic functions

Banach Center Publications

We introduce and discuss a new class of (multivalued analytic) transcendental functions which still share with algebraic functions the property that the number of their isolated zeros can be explicitly counted. On the other hand, this class is sufficiently rich to include all periods (integral of rational forms over algebraic cycles).

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