On the Summability of Formal Solutions of Nonlinear Partial Differential Equations with Shrinkings

We investigate the existence and Borel summability of formal power series in one variable with holomorphic coefficients, solutions of nonlinear partial differential equations with shrinkings having non-Kowalewski type in the complex domain. Sufficient conditions are given in terms of the shape of the functional partial differential equations and initial conditions. The existence and asymptotic behavior of local sectorial holomorphic solutions of these nonlinear functional partial differential equations are obtained as a by-product. We apply the results to the study of asymptotic the behavior of solutions of some advanced-argument partial differential equations in a neighborhood of infinity.