On Borel summation and Stokes phenomena for rank-\(1\) nonlinear systems of ordinary differential equations
The author studies in detail nonlinear systems of ordinary differential equations at an irregular singularity of rank 1, under nonresonance conditions. He shows that the formal asymptotic exponential series solutions are Borel summable in a generalized sense (i.e. in a sense in order that the summation is linear, multiplicative and commutes with differentiation and complex conjugation) along any direction in which the exponentials decay. The connection between local and classical Stokes phenomena is analyzed.
nonlinear systems of ordinary differential equations
scientific article; zbMATH DE number 1425119