Second-order viability result in Banach spaces

Myelkebir Aitalioubrahim; Said Sajid

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2010)

  • Volume: 30, Issue: 1, page 5-21
  • ISSN: 1509-9407

Abstract

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We show the existence result of viable solutions to the second-order differential inclusion ẍ(t) ∈ F(t,x(t),ẋ(t)), x(0) = x₀, ẋ(0) = y₀, x(t) ∈ K on [0,T], where K is a closed subset of a separable Banach space E and F(·,·,·) is a closed multifunction, integrably bounded, measurable with respect to the first argument and Lipschitz continuous with respect to the third argument.

How to cite

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Myelkebir Aitalioubrahim, and Said Sajid. "Second-order viability result in Banach spaces." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 30.1 (2010): 5-21. <http://eudml.org/doc/271139>.

@article{MyelkebirAitalioubrahim2010,
abstract = { We show the existence result of viable solutions to the second-order differential inclusion ẍ(t) ∈ F(t,x(t),ẋ(t)), x(0) = x₀, ẋ(0) = y₀, x(t) ∈ K on [0,T], where K is a closed subset of a separable Banach space E and F(·,·,·) is a closed multifunction, integrably bounded, measurable with respect to the first argument and Lipschitz continuous with respect to the third argument. },
author = {Myelkebir Aitalioubrahim, Said Sajid},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {differential inclusion,viability; measurability; selection},
language = {eng},
number = {1},
pages = {5-21},
title = {Second-order viability result in Banach spaces},
url = {http://eudml.org/doc/271139},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Myelkebir Aitalioubrahim
AU - Said Sajid
TI - Second-order viability result in Banach spaces
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2010
VL - 30
IS - 1
SP - 5
EP - 21
AB - We show the existence result of viable solutions to the second-order differential inclusion ẍ(t) ∈ F(t,x(t),ẋ(t)), x(0) = x₀, ẋ(0) = y₀, x(t) ∈ K on [0,T], where K is a closed subset of a separable Banach space E and F(·,·,·) is a closed multifunction, integrably bounded, measurable with respect to the first argument and Lipschitz continuous with respect to the third argument.
LA - eng
KW - differential inclusion,viability; measurability; selection
UR - http://eudml.org/doc/271139
ER -

References

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  5. [5] B. Cornet and G. Haddad, Théorème de viabilité pour les inclusions différentielles du seconde ordre, Isr. J. Math. 57 (2) (1987), 225-238. Zbl0659.34012
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  7. [7] T.X. Duc Ha, Existence of viable solutions for nonconvex-valued differential inclusions in Banach spaces, Portugaliae Mathematica 52 Fasc. 2, 1995. Zbl0824.34021
  8. [8] M. Larrieu, Invariance d'un fermé pour un champ de vecteurs de Carathéodory, Pub. Math. de Pau, 1981. 
  9. [9] V. Lupulescu, A viability result for second order differential inclusions, Electron J. Diff. Eq. 76 (2003), 1-12. Zbl1023.34010
  10. [10] V. Lupulescu, Existence of solutions for nonconvex second order differential inclusions, Applied Math. E-notes 3 (2003), 115-123. Zbl1034.34018
  11. [11] R. Morchadi and S. Sajid, Noncovex second-order differential inclusion, Bulletin of the Polish Academy of Sciences 47 (3) (1999). Zbl0943.34054
  12. [12] Q. Zhu, On the solution set of differential inclusions in Banach spaces, J. Differ. Eq. 41 (2001), 1-8. 

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