On \(q\)-asymptotics for linear \(q\)-difference-differential equations with Fuchsian and irregular singularities

DOI10.1016/j.jde.2012.01.038zbMath1251.35016arXiv1003.1104OpenAlexW2963622030MaRDI QIDQ414806

Javier Sanz, Stéphane Malek, Alberto Lastra Sedano

Publication date: 11 May 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.1104

zbMATH Keywords

small divisor\(q\)-difference-differential equation\(q\)-Gevrey asymptotic expansion\(q\)-Laplace transformformal power series solutionFuchsian and irregular singularities

Mathematics Subject Classification ID

Series solutions to PDEs (35C10) Laplace transform (44A10) Boundary value problems for linear first-order PDEs (35F15)

Related Items

q-Analogues of Laplace and Borel transforms by means of q-exponentials ⋮ On \(q\)-advanced spherical Bessel functions of the first kind and perturbations of the Haar wavelet ⋮ Meromorphic solutions of linear \(q\)-difference equations ⋮ Small divisors effects in some singularly perturbed initial value problem with irregular singularity ⋮ On sequences preserving \(q\)-Gevrey asymptotic expansions ⋮ Smooth wavelet approximations of truncated Legendre polynomials via the Jacobi theta function ⋮ On parametric multilevel \(q\)-Gevrey asymptotics for some linear \(q\)-difference-differential equations ⋮ On complex singularity analysis for some linear partial differential equations in \(\mathbb C^3\) ⋮ Solutions of a class of multiplicatively advanced differential equations ⋮ On a partial \(q\)-analog of a singularly perturbed problem with Fuchsian and irregular time singularities ⋮ On parametric Gevrey asymptotics for singularly perturbed partial differential equations with delays ⋮ Asymptotics and confluence for some linear \(q\)-difference-differential Cauchy problem ⋮ Solutions of a class of multiplicatively advanced differential equations. II: Fourier transforms ⋮ On the multiple-scale analysis for some linear partial \(q\)-difference and differential equations with holomorphic coefficients

Cites Work

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• On Gevrey functional solutions of partial differential equations with Fuchsian and irregular singularities
• On complex singularity analysis for linear \(q\)-difference-differential equations
• An elliptic equation with perturbed \(p\)-Laplace operator
• Unique summing of formal power series solutions to advanced and delayed differential equations
• About the growth of entire functions solutions of linear algebraic \(q\)- difference equations
• From divergent power series to analytic functions. Theory and application of multisummable power series
• On the Cauchy problem for non linear PDEs in the Gevrey class with shrinkings
• Analytic continuation into the \(FUTURE\)
• \(q\)-Gevrey asymptotic expansion and Jacobi theta function.
• On the use of Mellin transform to a class of \(q\)-difference-differential equations
• The method of Frobenius to Fuchsian partial differential equations
• Propagation of singularities for Fuchsian operators
• Multisummability of formal solutions of some linear partial differential equations
• Removable singularities of holomorphic solution of linear partial differential equations
• Summability of divergent series
• Formal power series and linear systems of meromorphic ordinary differential equations
• Small divisors and large multipliers
• On singularly perturbed partial integro-differential equations with irregular singularity
• On functional linear partial differential equations in Gevrey spaces of holomorphic functions
• A Cauchy-Kovalevskaja type theory in the Gevrey class for PDEs with shrinkings
• Existence and non-existence of null-solutions for some non-Fuchsian partial differential operators with T-dependent coefficients
• Problèmes de Cauchy pour des opérateurs singuliers
• ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF THE FUNCTIONAL DIFFERENTIAL EQUATION y′(x) = ay(λx) + by(x)
• Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity