Gevrey Order and Summability of Formal Series Solutions of Certain Classes of Inhomogeneous Linear Integro-Differential Equations with Variable Coefficients

摘要

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) is an element of 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.