Stephane MALEK
On the summability of formal solutions of linear partial differential equations
(344K, postscript)

ABSTRACT.  We investigate the existence and the Borel summability of formal power series in one variable with holomorphic coefficients, solutions to linear partial differential equations with non Kowalevskaya type in the complex domain. Sufficient conditions are given in terms of the shape of the partial differential equations and initial conditions. Existence and asymptotic behaviour of local sectorial holomorphic solutions to these linear partial differential equations are obtained as byproduct.