Title:
|
Existence results for boundary value problems for fourth-order differential inclusions with nonconvex valued right hand side (English) |
Author:
|
Arara, A. |
Author:
|
Benchohra, M. |
Author:
|
Ntouyas, Sotiris K. |
Author:
|
Ouahab, A. |
Language:
|
English |
Journal:
|
Archivum Mathematicum |
ISSN:
|
0044-8753 (print) |
ISSN:
|
1212-5059 (online) |
Volume:
|
40 |
Issue:
|
3 |
Year:
|
2004 |
Pages:
|
219-227 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
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. (English) |
Keyword:
|
differential inclusions |
Keyword:
|
contraction multivalued map |
Keyword:
|
fixed point |
Keyword:
|
decomposable values |
Keyword:
|
measurable |
MSC:
|
34A60 |
MSC:
|
34B15 |
MSC:
|
47H10 |
idZBL:
|
Zbl 1117.34005 |
idMR:
|
MR2107016 |
. |
Date available:
|
2008-06-06T22:43:37Z |
Last updated:
|
2012-05-10 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107904 |
. |
Reference:
|
[1] Aftabizadeh, A. R.: Existence and uniqueness theorems for fourth-order boundary value problems.J. Math. Anal. Appl. 116 (1986), 415–426. Zbl 0634.34009, MR 0842808 |
Reference:
|
[2] Agarwal, R.: On fourth-order boundary value problems arising in beam analysis.Differ. Integral Equ. 2 (1989), 91–110. Zbl 0715.34032, MR 0960017 |
Reference:
|
[3] Bressan, A. and Colombo, G.: Extensions and selections of maps with decomposable values.Studia Math. 90 (1988), 69–86. MR 0947921 |
Reference:
|
[3] Cabada, A.: 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. MR 1283059 |
Reference:
|
[5] Castaing, C. and Valadier, M.: Convex Analysis and Measurable Multifunctions.Lecture Notes in Mathematics, vol. 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. MR 0467310 |
Reference:
|
[6] Covitz, H. and Nadler, S. B., Jr.: Multivalued contraction mappings in generalized metric spaces.Israel J. Math. 8 (1970), 5–11. MR 0263062 |
Reference:
|
[7] De Coster, C., Fabry, C. and Munyamarere, F.: Nonresonance condition for fourth-order nonlinear boundary value problems.Int. J. Math. Math. Sci. 17 (1994), 725–740. MR 1298797 |
Reference:
|
[8] Deimling, K.: Multivalued Differential Equations.De Gruyter, Berlin, 1992. Zbl 0820.34009, MR 1189795 |
Reference:
|
[9] Del Pino, M. A. and Manasevich, R. F.: Existence for a fourth-order boundary value problem under a two-parameter nonresonance condition.Proc. Amer. Math. Soc. 112 (1991), 81–86. MR 1043407 |
Reference:
|
[10] Frigon, M. and Granas, A.: Théorèmes d’existence pour des inclusions différentielles sans convexité.C. R. Acad. Sci. Paris, Ser. I Math. 310 (1990), 819–822. MR 1058503 |
Reference:
|
[11] Gorniewicz, L.: Topological Fixed Point Theory of Multivalued Mappings.Math. Appl. 495, Kluwer Academic Publishers, Dordrecht, 1999. Zbl 1107.55001, MR 1748378 |
Reference:
|
[12] Hu, Sh. and Papageorgiou, N.: Handbook of Multivalued Analysis, Volume I: Theory.Kluwer Academic Publishers, Dordrecht, Boston, London, 1997. MR 1485775 |
Reference:
|
[13] Kisielewicz, M.: Differential Inclusions and Optimal Control.Kluwer, Dordrecht, The Netherlands, 1991. Zbl 0731.49001, MR 1135796 |
Reference:
|
[14] Korman, P.: A maximum principle for fourth-order ordinary differential equations.Appl. Anal. 33 (1989), 267–273. Zbl 0681.34016, MR 1030113 |
Reference:
|
[15] Ma, R. Y., Zhang, J. H. and Fu, M.: The method of lower and upper solutions for fourth-order two-point boundary value problem.J. Math. Anal. Appl. 215 (1997), 415–422. MR 1490759 |
Reference:
|
[16] Schroeder, J.: Fourth-order two-point boundary value problems; estimates by two-sided bounds.Nonlinear Anal. 8 (1984), 107–114. Zbl 0533.34019, MR 0734445 |
Reference:
|
[17] Smart, D. R.: Fixed Point Theorems.Cambridge Univ. Press, Cambridge, 1974. Zbl 0427.47036, MR 0467717 |
Reference:
|
[18] Švec, M.: Periodic boundary value problem for fourth order differential inclusions.Arch. Math. (Brno) 33 (1997), 167–171. MR 1464311 |
. |