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