Fixed point theorems for set-valued maps and existence principles for integral inclusions

Journal of Mathematical Analysis and Applications

Volumn 245, Issue 2, 2000, Pages 594-612

  O'Regan, Donal ^a   Precup, Radu ^b  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^b BABE BOLYAI UNIVERSITY   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034656497     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.6789     Document Type: Article

References (19)

1. Agarwal R. P., O'Regan D. Existence criteria for operator inclusions in abstract spaces. J. Comput. Appl. Math. 113:2000;183-193.
2. Appel J., De Pascale E., Nguyen H. T., Zabreiko P. P. Nonlinear integral inclusions of Hammerstein type. Topol. Methods Nonlinear Anal. 5:1995;111-124.
3. Aubin J. P., Cellina A. Differential Inclusions. 1984;Springer-Verlag, Berlin/Heidelberg/New York/Tokyo.
4. T. Cardinali, and, N. S. Papageorgiou, Hammerstein Integral Inclusions in Reflexive Banach Spaces, to appear.
5. Cellina A., Fryszkowski A., Rzezuchowski T. Upper semicontinuity of Nemytskij operators. Ann. Mat. Pura Appl. 160:1991;321-330.
6. Couchouron J. F., Kamenski M. A unified topological point of view for integro-differential inclusions. Differential Inclusions and Optimal Control. Lecture Notes in Nonlinear Analysis. 2:1998;. p. 123-137.
7. Deimling K. Nonlinear Functional Analysis. 1985;Spinger-Verlag, Berlin/Heidelberg/New York/Tokyo.
8. Deimling K. Multivalued Differential Equations. 1992;de Gruyter, Berlin/New York.
9. Frigon M. Théorèmes d'existence de solutions d'inclusions différentielles. Granas A., Frigon M., Topological Methods in Differential Equations and Inclusions. NATO ASI Series C. 472:1995;51-87 Kluwer Academic, Dordrecht/Boston/London.
10. Guo D., Lakshmikantham V., Liu X. Nonlinear Integral Equations in Abstract Spaces. 1996;Kluwer Academic, Dordrecht/Boston/London.
11. Heinz H. P. On the behaviour of measures of noncompactness with respect to diffferentiation and integration of vector-valued functions. Nonlinear Anal. 7:1983;1351-1371.
12. Hu S., Papageorgiou N. S. Handbook of Multivalued Analysis, Vol. I: Theory. 1997;Kluwer Academic, Dordrecht/Boston/London.
13. Mönch H. Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces. Nonlinear Anal. 4:1980;985-999.
14. Mönch H., Von Harten G. F. On the Cauchy problem for ordinary differential equations in Banach spaces. Arch. Math. (Basel). 39:1982;153-160.
15. O'Regan D. Multivalued integral equations in finite and infinite dimensions. Comm. Appl. Anal. 2:1998;487-496.
16. O'Regan D. Nonlinear alternatives for multivalued maps with applications to operator inclusions in abstract spaces. Proc. Amer. Math. Soc. 127:1999;3557-3564.
17. D. O'Regan, and, R. Precup, Existence criteria for integral equations in Banach spaces, J. Inequal. Appl, to appear.
18. D. O'Regan, and, R. Precup, Theorems of Leray-Schauder Type and Applications, Gordon and Breach, New York, in press.
19. R. Precup, Discrete continuation method for nonlinear integral equations in Banach spaces, Pure Math. Appl, to appear.