Existence results for boundary value problems for fourth-order differential inclusions with nonconvex valued right hand side

A. Arara; Mouffak Benchohra; Sotiris K. Ntouyas; Abdelghani Ouahab

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 3, page 219-227
  • ISSN: 0044-8753

Abstract

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In this paper a fixed point theorem due to Covitz and Nadler for contraction multivalued maps, and the Schaefer’s theorem combined with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued operators with decomposables values, are used to investigate the existence of solutions for boundary value problems of fourth-order differential inclusions.

How to cite

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Arara, A., et al. "Existence results for boundary value problems for fourth-order differential inclusions with nonconvex valued right hand side." Archivum Mathematicum 040.3 (2004): 219-227. <http://eudml.org/doc/249315>.

@article{Arara2004,
abstract = {In this paper a fixed point theorem due to Covitz and Nadler for contraction multivalued maps, and the Schaefer’s theorem combined with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued operators with decomposables values, are used to investigate the existence of solutions for boundary value problems of fourth-order differential inclusions.},
author = {Arara, A., Benchohra, Mouffak, Ntouyas, Sotiris K., Ouahab, Abdelghani},
journal = {Archivum Mathematicum},
keywords = {differential inclusions; contraction multivalued map; fixed point; decomposable values; measurable; contraction multivalued map; fixed point; decomposable values},
language = {eng},
number = {3},
pages = {219-227},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Existence results for boundary value problems for fourth-order differential inclusions with nonconvex valued right hand side},
url = {http://eudml.org/doc/249315},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Arara, A.
AU - Benchohra, Mouffak
AU - Ntouyas, Sotiris K.
AU - Ouahab, Abdelghani
TI - Existence results for boundary value problems for fourth-order differential inclusions with nonconvex valued right hand side
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 3
SP - 219
EP - 227
AB - In this paper a fixed point theorem due to Covitz and Nadler for contraction multivalued maps, and the Schaefer’s theorem combined with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued operators with decomposables values, are used to investigate the existence of solutions for boundary value problems of fourth-order differential inclusions.
LA - eng
KW - differential inclusions; contraction multivalued map; fixed point; decomposable values; measurable; contraction multivalued map; fixed point; decomposable values
UR - http://eudml.org/doc/249315
ER -

References

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  1. Existence and uniqueness theorems for fourth-order boundary value problems, J. Math. Anal. Appl. 116 (1986), 415–426. Zbl0634.34009MR0842808
  2. On fourth-order boundary value problems arising in beam analysis, Differ. Integral Equ. 2 (1989), 91–110. Zbl0715.34032MR0960017
  3. Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69–86. MR0947921
  4. The method of lower and upper solutions for second, third, fourth, and higher order boundary value problem, J. Math. Anal. Appl. 248 (2000), 195–202. MR1283059
  5. Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, vol. 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. MR0467310
  6. Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5–11. MR0263062
  7. Nonresonance condition for fourth-order nonlinear boundary value problems, Int. J. Math. Math. Sci. 17 (1994), 725–740. MR1298797
  8. Multivalued Differential Equations, De Gruyter, Berlin, 1992. Zbl0820.34009MR1189795
  9. Existence for a fourth-order boundary value problem under a two-parameter nonresonance condition, Proc. Amer. Math. Soc. 112 (1991), 81–86. MR1043407
  10. Théorèmes d’existence pour des inclusions différentielles sans convexité, C. R. Acad. Sci. Paris, Ser. I Math. 310 (1990), 819–822. MR1058503
  11. Topological Fixed Point Theory of Multivalued Mappings, Math. Appl. 495, Kluwer Academic Publishers, Dordrecht, 1999. Zbl1107.55001MR1748378
  12. Handbook of Multivalued Analysis, Volume I: Theory, Kluwer Academic Publishers, Dordrecht, Boston, London, 1997. MR1485775
  13. Differential Inclusions and Optimal Control, Kluwer, Dordrecht, The Netherlands, 1991. Zbl0731.49001MR1135796
  14. A maximum principle for fourth-order ordinary differential equations, Appl. Anal. 33 (1989), 267–273. Zbl0681.34016MR1030113
  15. The method of lower and upper solutions for fourth-order two-point boundary value problem, J. Math. Anal. Appl. 215 (1997), 415–422. MR1490759
  16. Fourth-order two-point boundary value problems; estimates by two-sided bounds, Nonlinear Anal. 8 (1984), 107–114. Zbl0533.34019MR0734445
  17. Fixed Point Theorems, Cambridge Univ. Press, Cambridge, 1974. Zbl0427.47036MR0467717
  18. Periodic boundary value problem for fourth order differential inclusions, Arch. Math. (Brno) 33 (1997), 167–171. MR1464311

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