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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:
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


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