| Title:
|
On fourth-order boundary-value problems (English) |
| Author:
|
Aitalioubrahim, Myelkebir |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
5-16 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show the existence of solutions to a boundary-value problem for fourth-order differential inclusions in a Banach space, under Lipschitz’s contractive conditions, Carathéodory conditions and lower semicontinuity conditions. (English) |
| Keyword:
|
Boundary-value problems |
| Keyword:
|
set-valued map |
| Keyword:
|
fixed point |
| Keyword:
|
selection |
| MSC:
|
34B15 |
| MSC:
|
34G20 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 1236.34087 |
| idMR:
|
MR2797518 |
| . |
| Date available:
|
2010-09-13T06:50:54Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140730 |
| . |
| 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, 10.1016/S0022-247X(86)80006-3 |
| Reference:
|
[2] Bressan, A., Colombo, G.: Extensions and selections of maps with decomposable values.Studia Math. 90 (1988), 69–86. Zbl 0677.54013, MR 0947921 |
| Reference:
|
[3] Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions.Lecture Notes in Mathematics 580 Spriger, New York–Berlin–Heidelberg, 1977. Zbl 0346.46038, MR 0467310, 10.1007/BFb0087688 |
| Reference:
|
[4] Covitz, H., Nadler, S. B. Jr.: Multivalued contraction mappings in generalized metric spaces.Israel J. Math. 8 (1970), 5–11. MR 0263062, 10.1007/BF02771543 |
| Reference:
|
[5] Frigon, M., 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:
|
[6] Hu, S., Papageorgiou, N. S.: Handbook of Multivalued Analysis, Vol. I: Theory.Kluwer, Dordrecht, 1997. MR 1485775 |
| Reference:
|
[7] Lasota, A., Opial, Z.: An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations.Bull. Acad. Polon. Sci., Ser. Math. Astronom. Phys. 13 (1965), 781–786. Zbl 0151.10703, MR 0196178 |
| Reference:
|
[8] Liu, Y.: Multiple positive solutions to fourth-order singular boundary-value problems in abstract spaces.Electron. J. Differential Equations 120 (2004), 1–13. Zbl 1076.34068, MR 2108891 |
| Reference:
|
[9] Martelli, M.: A Rothe’s type theorem for noncompact acyclic-valued map.Boll. Un. Mat. Ital. 11 (1975), 70–76. MR 0394752 |
| Reference:
|
[10] Smart, D. R.: Fixed Point Theorems.Cambridge Univ. Press, Cambridge, 1974. Zbl 0297.47042, MR 0467717 |
| Reference:
|
[11] Yang, Y.: Fourth-order two-point boundary value problems.Proc. Amer. Math. Soc. 104 (1988), 175–180. Zbl 0671.34016, MR 0958062, 10.1090/S0002-9939-1988-0958062-3 |
| Reference:
|
[12] Zhu, Q.: On the solution set of differential inclusions in Banach spaces.J. Differential Equations 93, 2 (1991), 213–237. MR 1125218, 10.1016/0022-0396(91)90011-W |
| . |
