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Formal and Analytic Solutions of Diff. Equations

FASdiff, Alcalá de Henares, Spain, September 2017, Selected, Revised Contributions

  • Conference proceedings
  • © 2018

Overview

Editors:
  1. Galina Filipuk

    1. Institute of Mathematics, University of Warsaw, Warsaw, Poland

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    You can also search for this editor in PubMed   Google Scholar

  2. Alberto Lastra

    1. Departamento de Física y Matemáticas, University of Alcalá, Alcalá de Henares, Spain

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    You can also search for this editor in PubMed   Google Scholar

  3. Sławomir Michalik

    1. Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszynski University, Warsaw, Poland

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 256)

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Table of contents (16 papers)

  1. Front Matter

    Pages i-xii
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  2. A Survey on the Elements of Nonlinear Analysis

    1. Front Matter

      Pages 1-1
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    2. Elements of Nonlinear Analysis

      • Alexander D. Bruno
      Pages 3-23

  3. Summability of Divergent Solutions of PDEs

    1. Front Matter

      Pages 25-25
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    2. On the k-Summability of Formal Solutions for a Class of Higher Order Partial Differential Equations with Time-Dependent Coefficients

      • Kunio Ichinobe
      Pages 27-45

    3. Singular Solutions to a System of Equations related to Ricci-Flat Kähler Metrics

      • Jose Ernie C. Lope, Mark Philip F. Ona
      Pages 47-59

    4. Hyperasymptotic Solutions for Certain Partial Differential Equations

      • Sławomir Michalik, Maria Suwińska
      Pages 61-78

    5. The Stokes Phenomenon for Certain PDEs in a Case When Initial Data Have a Finite Set of Singular Points

      • Bożena Tkacz
      Pages 79-93

    6. Soliton Resolution for the Focusing Integrable Discrete Nonlinear Schrödinger Equation

      • Hideshi Yamane
      Pages 95-102

    7. Complicated and Exotic Expansions of Solutions to the Painlevé Equations

      • Alexander D. Bruno
      Pages 103-145

  4. Summability of Divergent Solutions of ODEs

    1. Front Matter

      Pages 147-147
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    2. The Borel Transform of Canard Values and Its Singularities

      • P. Pavis d’Escurac
      Pages 149-175

    3. Quantization Conditions on Riemannian Surfaces and Spectral Series of Non-selfadjoint Operators

      • Andrei Shafarevich
      Pages 177-187

    4. Semilocal Monodromy of Rigid Local Systems

      • Toshio Oshima
      Pages 189-199

    5. On the Newton Polygon of a Moser-Irreducible Linear Differential System

      • Moulay Barkatou
      Pages 201-218

  5. Related Topics

    1. Front Matter

      Pages 219-219
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    2. Uniqueness Property for \(\rho \)-Analytic Functions

      • Grzegorz Łysik
      Pages 221-226

    3. On the Algebraic Study of Asymptotics

      • Naofumi Honda, Luca Prelli
      Pages 227-237

    4. Deformations with a Resonant Irregular Singularity

      • Davide Guzzetti
      Pages 239-250

    5. Symmetric Semi-classical Orthogonal Polynomials of Class One on q-Quadratic Lattices

      • Galina Filipuk, Maria das Neves Rebocho
      Pages 251-261
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  1. Formal and Analytic Solutions of Diff. Equations

Keywords

About this book

These proceedings provide methods, techniques, different mathematical tools and recent results in the study of formal and analytic solutions to Diff. (differential, partial differential, difference, q-difference, q-difference-differential.... ) Equations.  They consist of selected contributions from the conference "Formal and Analytic Solutions of Diff.  Equations", held at Alcalá de Henares, Spain during September 4-8, 2017. Their topics include summability and asymptotic study of both ordinary and partial differential equations. The volume is divided into four parts. The first paper is a survey of the elements of nonlinear analysis. It describes the algorithms to obtain asymptotic expansion of solutions of nonlinear algebraic, ordinary differential, partial differential equations, and of systems of such equations. Five works on formal and analytic solutions of PDEs are followed by five papers on the study of solutions of ODEs. The proceedings conclude withfive works on related topics, generalizations and applications. All contributions have been peer reviewed by anonymous referees chosen among the experts on the subject.

The volume will be of interest to graduate students and researchers in theoretical and applied mathematics, physics and engineering seeking an overview of the recent trends in the theory of formal and analytic solutions of functional (differential, partial differential, difference, q-difference, q-difference-differential) equations in the complex domain.


Editors and Affiliations

  • Institute of Mathematics, University of Warsaw, Warsaw, Poland

    Galina Filipuk

  • Departamento de Física y Matemáticas, University of Alcalá, Alcalá de Henares, Spain

    Alberto Lastra

  • Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszynski University, Warsaw, Poland

    Sławomir Michalik

Bibliographic Information

  • Book Title: Formal and Analytic Solutions of Diff. Equations

  • Book Subtitle: FASdiff, Alcalá de Henares, Spain, September 2017, Selected, Revised Contributions

  • Editors: Galina Filipuk, Alberto Lastra, Sławomir Michalik

  • Series Title: Springer Proceedings in Mathematics & Statistics

  • DOI: https://doi.org/10.1007/978-3-319-99148-1

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2018

  • Hardcover ISBN: 978-3-319-99147-4Published: 25 September 2018

  • Softcover ISBN: 978-3-030-07570-5Published: 20 December 2018

  • eBook ISBN: 978-3-319-99148-1Published: 24 September 2018

  • Series ISSN: 2194-1009

  • Series E-ISSN: 2194-1017

  • Edition Number: 1

  • Number of Pages: XII, 274

  • Number of Illustrations: 31 b/w illustrations, 6 illustrations in colour

  • Topics: Partial Differential Equations, Difference and Functional Equations

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