In this paper, we consider the class of so-called weakly hyperbolic linear systems, which includes correct and hyperbolic (exponentially-dichotomous) systems. We prove new results generalizing related classical theorems on the conditional stability of solutions. We establish the existence of stable manifolds consisting of points corresponding to the solutions of such systems with negative Lyapunov exponents. We study the behavior of solutions starting outside the stable manifold. The technique used in our paper is similar to that in the theory of hyperbolic systems.

Original languageEnglish
Pages (from-to)635-643
Number of pages9
JournalMathematical Notes
Volume75
Issue number5-6
StatePublished - 1 May 2004

    Research areas

  • Grobman correctness coefficient, Stability problem, Stable manifold, Weakly nonlinear hyperbolic system

    Scopus subject areas

  • Mathematics(all)

ID: 41279506