Lyapunov functions in justification theorems for asymptotics
Leonid Anatol'evich Kalyakin · Mathematical Notes · 2015
A formal asymptotic solution is considered for a nonlinear system of ordinary differential equations in a neighborhood of a singular point. The problem of existence of an exact solution with such an asymptotics and the problem of stability of this solution are solved. The main tool in these studies is the Lyapunov function for a system linearized on a formal solution.