Formal power series solutions with coefficients defined on shrinking discs for some partial differential equations

2025/12/06 by Lastra, Alberto, Michalik, Sławomir, Suwińska, Maria
Computer Science · Mathematics · #Polynomial and algebraic computation #Meromorphic and Entire Functions #Algebraic and Geometric Analysis

paper · doi:10.48550/arxiv.2512.06470

Abstract

In this paper conditions, under which an integro-differential operator is a linear automorphism, are provided. Alternatively, the problem can be considered in terms of existence of a unique formal power series solution for a linear Cauchy problem, where the coefficients of the solution are of a certain Gevrey order on progressively shrinking domains.

Citations

• On parametric 0-Gevrey asymptotic expansions in two levels for some linear partial q-difference-differential equations
• q-Nagumo norms and formal solutions to singularly perturbed q-difference equations
• On conditions determining formal automorphisms of integro-differential operators
• Summability of formal solutions for some generalized moment partial differential equations
• Maillet type theorem for nonlinear totally characteristic partial differential equations

Related

• On conditions determining formal automorphisms of integro-differential operators
• Investigation of the solutions of the Cauchy problem and boundary-value problems for the ordinary differential equations with continuously changing order of the derivative
• On a class of formal power series and their summability
• Linear differential equations and Hurwitz series
• Reprint: On algebraic differential equations satisfied by automorphic functions (1969)