Gevrey Order and Summability of Formal Series Solutions of Certain Classes of Inhomogeneous Linear Integro-Differential Equations with Variable Coefficients |
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Authors: | Pascal Remy |
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Affiliation: | 1.Lycée Les Pierres Vives,Carrières-sur-Seine,France |
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Abstract: | 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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