Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. III. Parabolic equations and delay systems

Abstract

This is the third part in a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. The current part focuses on applications of general theory, developed in the authors' paper "Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory," Trans. Amer. Math. Soc. 365 (2013), pp. 5329-5365, to positive continuous-time random dynamical systems on infinite dimensional ordered Banach spaces arising from random parabolic equations and random delay systems. It is shown under some quite general assumptions that measurable linear skew-product semidynamical systems generated by random parabolic equations and by cooperative systems of linear delay differential equations admit measurable families of generalized principal Floquet subspaces, and generalized principal Lyapunov exponents.

41 pages

References in corpus (5)

• Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory
• Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. II. Finite-dimensional systems
• Tensor Products, Positive Linear Operators, and Delay-Differential Equations
• Globally positive solutions of linear parabolic PDE's of second order with Robin boundary conditions
• Globally positive solutions of linear parabolic partial differential equations of second order with Dirichlet boundary conditions

Cited by in corpus (4)

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