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

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2007)

- Volume: 27, Issue: 2, page 315-327
- ISSN: 1509-9407

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topA. Sikorska-Nowak. "Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.2 (2007): 315-327. <http://eudml.org/doc/271205>.

@article{A2007,

abstract = {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.},

author = {A. Sikorska-Nowak},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {pseudo-solution; Pettis integral; Henstock-Kurzweil integral; Henstock-Kurzweil-Pettis integral; Cauchy problem},

language = {eng},

number = {2},

pages = {315-327},

title = {Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals},

url = {http://eudml.org/doc/271205},

volume = {27},

year = {2007},

}

TY - JOUR

AU - A. Sikorska-Nowak

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

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2007

VL - 27

IS - 2

SP - 315

EP - 327

AB - 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.

LA - eng

KW - pseudo-solution; Pettis integral; Henstock-Kurzweil integral; Henstock-Kurzweil-Pettis integral; Cauchy problem

UR - http://eudml.org/doc/271205

ER -

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