In this short monograph we present a new reformulation of the direct method for stability of nonlinear ordinary differential systems, often called Lyapunov’s second method. The main idea is to construct appropriate auxiliary functions to study the stability without recourse to the explicit form of solutions, or examine the linear approximation of the nonlinear system under consideration. Our theory is so elastic to cover not only very singular second order ordinary differential systems, but also second order partial differential systems of hyperbolic and parabolic type. Our results for stability are new also for scalar equations of canonical form and even in the linear case. For this reason, in order to present the main ideas in clarity, in the first part of the volume we discuss the simplest typical protype we cover.
Lectures on Stability.
PUCCI, Patrizia;
1995
Abstract
In this short monograph we present a new reformulation of the direct method for stability of nonlinear ordinary differential systems, often called Lyapunov’s second method. The main idea is to construct appropriate auxiliary functions to study the stability without recourse to the explicit form of solutions, or examine the linear approximation of the nonlinear system under consideration. Our theory is so elastic to cover not only very singular second order ordinary differential systems, but also second order partial differential systems of hyperbolic and parabolic type. Our results for stability are new also for scalar equations of canonical form and even in the linear case. For this reason, in order to present the main ideas in clarity, in the first part of the volume we discuss the simplest typical protype we cover.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
