Posts by Radu Precup


We present fixed point theorems for weakly sequentially upper semicontinuous decomposable non-convex-valued maps.They are based on an extension of the Arino-Gautier-Penot Fixed Point Theorem for weakly sequentially upper semicontinuous maps with convex values. Applications are given to abstract operator inclusions in \(L_p\) spaces. An example is included to illustrate the theory.


Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania


Multi-valued map; operator inclusion; functional-differential inclusion; fixed point; continuation principle; measure of non-compactness; weak topology.

Paper coordinates

R. Precup, Fixed point theorems for decomposable multi-valued maps and applications, Zeit. Anal. Anwendungen 22 (2003), 843-861,


About this paper


Zeitschrift fur Analysis und ihre Anwendungen

Publisher Name
Print ISSN
Online ISSN



google scholar link

[1] Andres, J. and R. Bader: Asymptotic boundary value problems in Banach spaces. J. Math. Anal. Appl. 274 (2002), 437 – 457.
[2] Arino, O., Gautier, S. and J. P. Penot: A fixed point theorem for sequentially continuous maps with application to ordinary differential equations. Funkcial. Ekvac. 27 (1984), 273 – 279.
[3] Bader, R.: A topological fixed-point index theory for evolution inclusions. Z. Anal. Anw. 20 (2001), 3 – 15.
[4] Couchouron, J.-F. and M. Kamenskii: An abstract topological point of view and a general averaging principle in the theory of differential inclusions. Nonlin. Anal. 42 (2000), 1101 – 1129.
[5] Couchouron, J.-F. and R. Precup: Existence principles for inclusions of Hammerstein type involving noncompact acyclic multivalued maps. Electron. J. Diff. Equ. 2002 (2002), No. 04, 1 – 21.
[6] Couchouron, J.-F. and R. Precup: Anti-periodic solutions for second order differential inclusions (to appear).
[7] De Blasi, F. S.: On a property of the unit sphere in Banach spaces. Bull. Math. Soc. Sci. Math. Roum. 21 (1977), 259 – 262.
[8] Deimling, K.: Nonlinear Functional Analysis. Berlin et al.: Springer-Verlag 1985.
[9] Deimling, K.: Multivalued Differential Equations. Berlin – New York: Walter De Gruyter 1992.
[10] Diestel, J., Ruess, W. M. and W. Schachermayer: Weak compactness in L1(µ,X). Proc. Amer. Math. Soc. 118 (1993), 447-453.
[11] Dunford, N. and J. T. Schwartz: Linear Operators. Part I: General Theory. New York: Intersci. 1957.
[12] Gorniewicz, L.: Topological approach to differential inclusions. In: Topological Methods in Differential Equations and Inclusions (NATO ASI Series C 472;  eds.: A. Granas and M. Frigon). Dordrecht: Kluwer Acad. Publ. 1995, pp. 129 – 190.
[13] Guo, D., Lakshmikantham, V. and X. Liu: Nonlinear Integral Equations in Abstract Spaces. Dordrecht – Boston – London: Kluwer Acad. Publ. 1996.
[14] Hu, S. and N. S. Papageorgiou: Handbook of Multivalued Analysis. Vol. I: Theory. Dordrecht – Boston – London: Kluwer Acad. Publ. 1997.
[15] Hu, S. and N. S. Papageorgiou: Handbook of Multivalued Analysis. Vol. II: Applications. Dordrecht – Boston – London: Kluwer Acad. Publ. 2000.
[16] Kamenskii, M., Obukhovskii, V. and P. Zecca: Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces. Berlin – New York: Walter de Gruyter 2001.
[17] Monch, H.: Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces. Nonlin. Anal. 4 (1980), 985 – 999.
[18] O’Regan, D.: Fixed point theory of M¨onch type for weakly sequentially upper semicontinuous maps. Bull. Austral. Math. Soc. 61 (2000), 439 – 449.
[19] O’Regan, D. and R. Precup: Fixed point theorems for set-valued maps and existence principles for integral inclusions. J. Math. Anal. Appl. 245 (2000), 594 – 612.
[20] O’Regan, D. and R. Precup: Theorems of Leray-Schauder Type and Applications. Amsterdam: Gordon and Breach Sci. Publ. 2001.
[21] O’Regan, D. and R. Precup: Existence theory for nonlinear operator equations of Hammerstein type in Banach spaces. J. Dyn. Syst. Appl. (to appear).
[22] Precup, R.: Methods in Nonlinear Integral Equations. Dordrecht – Boston -London: Kluwer Acad. Publ. 2002.
[23] Vrabie, I. I.: Compactness Methods for Nonlinear Evolutions. Harlow: Longman Sci. & Techn. 1987.

Related Posts