Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals

Sikorska-Nowak, A.

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 27 (2007) no. 2, pp. 315-327.

Résumé

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.

Détail

Keywords: pseudo-solution, Pettis integral, Henstock-Kurzweil integral, Henstock-Kurzweil-Pettis integral, Cauchy problem

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