Stability in the almost everywhere sense: A linear transfer operator approach

R. Rajaram, U. Vaidya, M. Fardad, B. Ganapathysubramanian

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


The problem of almost everywhere stability of a nonlinear autonomous ordinary differential equation is studied using a linear transfer operator framework. The infinitesimal generator of a linear transfer operator (Perron-Frobenius) is used to provide stability conditions of an autonomous ordinary differential equation. It is shown that almost everywhere uniform stability of a nonlinear differential equation, is equivalent to the existence of a non-negative solution for a steady state advection type linear partial differential equation. We refer to this non-negative solution, verifying almost everywhere global stability, as Lyapunov density. A numerical method using finite element techniques is used for the computation of Lyapunov density.

Original languageEnglish (US)
Pages (from-to)144-156
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Aug 2010


  • Advection equation
  • Almost everywhere stability
  • Density function

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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