On a nonconvex boundary value problem for a first order multivalued differential system

Aurelian Cernea

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 3, page 237-244
  • ISSN: 0044-8753

Abstract

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We consider a boundary value problem for first order nonconvex differential inclusion and we obtain some existence results by using the set-valued contraction principle.

How to cite

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Cernea, Aurelian. "On a nonconvex boundary value problem for a first order multivalued differential system." Archivum Mathematicum 044.3 (2008): 237-244. <http://eudml.org/doc/250461>.

@article{Cernea2008,
abstract = {We consider a boundary value problem for first order nonconvex differential inclusion and we obtain some existence results by using the set-valued contraction principle.},
author = {Cernea, Aurelian},
journal = {Archivum Mathematicum},
keywords = {boundary value problem; differential inclusion; contractive set-valued map; fixed point; boundary value problem; differential inclusion; contractive set-valued map; fixed point},
language = {eng},
number = {3},
pages = {237-244},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On a nonconvex boundary value problem for a first order multivalued differential system},
url = {http://eudml.org/doc/250461},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Cernea, Aurelian
TI - On a nonconvex boundary value problem for a first order multivalued differential system
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 3
SP - 237
EP - 244
AB - We consider a boundary value problem for first order nonconvex differential inclusion and we obtain some existence results by using the set-valued contraction principle.
LA - eng
KW - boundary value problem; differential inclusion; contractive set-valued map; fixed point; boundary value problem; differential inclusion; contractive set-valued map; fixed point
UR - http://eudml.org/doc/250461
ER -

References

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  1. Boucherif, A., Merabet, N. Chiboub-Fellah, Boundary value problems for first order multivalued differential systems, Arch. Math. (Brno) 41 (2005), 187–195. (2005) MR2164669
  2. Castaing, C., Valadier, M., Convex Analysis and Measurable Multifunctions, Springer-Verlag, Berlin, 1977. (1977) Zbl0346.46038MR0467310
  3. Cernea, A., Existence for nonconvex integral inclusions via fixed points, Arch. Math. (Brno) 39 (2003), 293–298. (2003) Zbl1113.45014MR2032102
  4. Cernea, A., An existence result for nonlinear integrodifferential inclusions, Comm. Appl. Nonlinear Anal. 14 (2007), 17–24. (2007) MR2364691
  5. Cernea, A., On the existence of solutions for a higher order differential inclusion without convexity, Electron. J. Qual. Theory Differ. Equ. 8 (2007), 1–8. (2007) Zbl1123.34046MR2295686
  6. Covitz, H., Nadler jr., S. B., 10.1007/BF02771543, Israel J. Math. 8 (1970), 5–11. (1970) MR0263062DOI10.1007/BF02771543
  7. Kannai, Z., Tallos, P., Stability of solution sets of differential inclusions, Acta Sci. Math. (Szeged) 61 (1995), 197–207. (1995) Zbl0851.34015MR1377359
  8. Lim, T. C., 10.1016/0022-247X(85)90306-3, J. Math. Anal. Appl. 110 (1985), 436–441. (1985) Zbl0593.47056MR0805266DOI10.1016/0022-247X(85)90306-3
  9. Tallos, P., A Filippov-Gronwall type inequality in infinite dimensional space, Pure Math. Appl. 5 (1994), 355–362. (1994) MR1343457

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