Gevrey order and summability of formal series solutions of certain classes of inhomogeneous linear integro-differential equations with variable coefficients

Pascal Remy (1, 2)

1 Chercheur indépendant
2 LMV - Laboratoire de Mathématiques de Versailles

In this article, we investigate Gevrey and summability properties of formal power series solutions of certain classes of inhomogeneous linear integro-differential equations with analytic coefficients in a neighborhood of $(0,0)\in\mathbb{C}^{2}$. 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.

Mots clés: Linear integro-differential equation; divergent power series; Newton polygon; Gevrey order; summability

Domaines: Systèmes dynamiques [math.DS]

Pascal Remy. Gevrey order and summability of formal series solutions of certain classes of inhomogeneous linear integro-differential equations with variable coefficients. 2016. ⟨hal-01267736⟩