Random functional-differential inclusions with nonconvex right-hand side in a Banach space
Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals
We prove an existence theorem for the equation x' = f(t,xₜ), x(Θ) = φ(Θ), where xₜ(Θ) = x(t+Θ), for -r ≤ Θ < 0, t ∈ Iₐ, Iₐ = [0,a], a ∈ R₊ in a Banach space, using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of the measure of weak noncompactness.
Robustness with respect to small time-varied delay for linear dynamical systems on Banach spaces
Under suitable conditions we prove the wellposedness of small time-varied delay equations and then establish the robust stability for such systems on the phase space of continuous vector-valued functions.