Opuscula Math. 35, no. 5 (2015), 825-845
Parametric Borel summability for some semilinear system of partial differential equations
Abstract. In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with \(n\) independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002), 313-322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singular perturbation parameter for a linear equation with one independent variable. We shall extend their results to a semilinear system of equations with general independent variables.
Keywords: Borel summability, singular perturbation, Euler type operator.
Mathematics Subject Classification: 35C10, 45E10, 35Q15.