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

Alberto Lastra; Sławomir Michalik; Maria Suwińska

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arXiv · 2512.06470

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

Alberto Lastra·Sławomir Michalik·Maria Suwińska

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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.

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Alberto Lastra, Sławomir Michalik, Maria Suwińska. 2025-12-06. Formal power series solutions with coefficients defined on shrinking discs for some partial differential equations. https://arxiv.org/abs/2512.06470

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