On exponentially small terms of solutions to nonlinear ordinary differential equations

A. Tovbis
1994 Methods and Applications of Analysis  
The subject of the paper is exponential asymptotics, or in the other terminology, "asymptotics beyond all orders", to solutions of nonlinear ordinary differential equations. We present expressions for exponential corrections to the power series asymptotics of solutions under some generic assumptions on a given equation. We also discuss relations between exponential corrections and analytic properties of the Borel transform of the formal asymptotic series. In particular, we consider the Stokes
more » ... enomenon and show that the transition constant (the magnitude of the exponentially small "jump") is the same for all solutions which possess the same power series asymptotics in the considered region on the complex plane.
doi:10.4310/maa.1994.v1.n1.a5 fatcat:wysqg6n5hrbujp5we46j6davpq