Summability of the formal power series solutions of a certain class of inhomogeneous nonlinear partial differential equations with a single level - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Differential Equations Année : 2022

Summability of the formal power series solutions of a certain class of inhomogeneous nonlinear partial differential equations with a single level

Pascal Rémy

Résumé

In this article, we investigate the summability of the formal power series solutions in time of a class of inhomogeneous nonlinear partial differential equations in two variables, whose the attached Newton polygon admits a unique positive slope k, the latter being determined by the highest spatial-derivative order of the initial equation. We give in particular a necessary and sufficient condition for the k-summability of the solutions in a given direction, and we illustrate this result by some examples. This condition generalizes the ones already given by the author in the linear case [1,2] and, more recently, in the semilinear case [3,4]. In addition, we present some technical results on the generalized binomial and multinomial coefficients, which are needed for the proof of our main result.
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Dates et versions

hal-03993018 , version 1 (27-03-2023)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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Pascal Rémy. Summability of the formal power series solutions of a certain class of inhomogeneous nonlinear partial differential equations with a single level. Journal of Differential Equations, 2022, 313, pp.450-502. ⟨10.1016/j.jde.2022.01.006⟩. ⟨hal-03993018⟩
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