The Hukuhara-Kneser property for parabolic systems with nonlinear boundary conditions

We analyze the asymptotic behavior as x → ∞ of the product integral Π_x0^xe^A(s)ds, where A(s) is a perturbation of a diagonal matrix function by an integrable function on x₀,∞). Our results give information concerning the asymptotic behavior of solutions of certain linear ordinary differential equations, e.g., the second order equation y″ = a(x)y.