Sobre alguns critérios de C- estabilidade para sistemas de equações diferenciais

Abstract

The Mathematical Stability Theory for differential equations is a fundamental part of Mathematics and Theoretical Mechanics and has its beginnings in the late nineteenth century, being its founder the mathematician Lyapunov, who devoted to this subject a cycle of works, where his doctoral thesis "General Problem on the Stability of Motion" stands out. In this thesis Lyapunov shows the ...cases in which the first approximation really solves the stability question... The problem of stability of motion of systems with a finite number of degrees of freedom reduces, according to Lyapunov, to the investigation of the stability of the trivial (unperturbed) solution rcj = x2 = - - ■ - xn = 0 of the system of differential equations The present paper consists of the introduction, four chapters, conclusion, recommendations, and bibliography cited. The first chapter discusses the general properties of systems of differential equations. Then the OstrogradskiT-Liouville formula is studied. The Cauchy function is studied here. In this chapter the formulation and demonstration of the Grõnwall-Bellman lemma is proceeded. (TRADUÇÃO NOSSA)