Gevrey Properties and Summability of Formal Power Series Solutions of Some Inhomogeneous Linear Cauchy-Goursat Problems View Full Text


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Article Info

DATE

2019-02-11

AUTHORS

Pascal Remy

ABSTRACT

In this article, we investigate the Gevrey and summability properties of the formal power series solutions of some inhomogeneous linear Cauchy-Goursat problems with analytic coefficients in a neighborhood of (0,0)∈ℂ2. In particular, we give necessary and sufficient conditions under which these solutions are convergent or are k-summable, for a convenient positive rational number k, in a given direction. More... »

PAGES

1-40

References to SciGraph publications

  • 2017-10. Gevrey Order and Summability of Formal Series Solutions of Certain Classes of Inhomogeneous Linear Integro-Differential Equations with Variable Coefficients in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2015-12. On parametric multisummable formal solutions to some nonlinear initial value Cauchy problems in ADVANCES IN DIFFERENCE EQUATIONS
  • 2007-07. On Singularly Perturbed Partial Integro-Differential Equations with Irregular Singularity in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2010-10. Summability and fractional linear partial differential equations in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2016-10. Gevrey Order and Summability of Formal Series Solutions of some Classes of Inhomogeneous Linear Partial Differential Equations with Variable Coefficients in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2007-01. On the Summability of Formal Solutions of Nonlinear Partial Differential Equations with Shrinkings in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2010-07. On gevrey asymptotics for some nonlinear integro-differential equations in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2012-01. Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2012-01. On the summability of formal solutions for doubly singular nonlinear partial differential equations in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2008-07. On the Stokes Phenomenon for Holomorphic Solutions of Integro-Differential Equations with Irregular Singularity in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2009-04. On Gevrey functional solutions of partial differential equations with Fuchsian and irregular singularities in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2005-07. On the Summability of Formal Solutions of Linear Partial Differential Equations in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
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    http://scigraph.springernature.com/pub.10.1007/s10883-019-9428-0

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    http://dx.doi.org/10.1007/s10883-019-9428-0

    DIMENSIONS

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