Existence results for semi-linear integrodifferential inclusions with nonlocal conditions

Rocky Mountain Journal of Mathematics

Volumn 34, Issue 3, 2004, Pages 833-848

  Benchohra, M ^a   Gatsori, E P ^b   Ntouyas, S K ^b  

^a UNIVERSITY OF SIDI BEL ABBES   (Algeria)

^b UNIVERSITY OF IOANNINA   (Greece)

Author keywords

Contraction multi valued map; Existence; Fixed point; Measurable selection; Mild solution; Nonlocal condition; Semi linear differential inclusions

Indexed keywords

EID: 5644300632     PISSN: 00357596     EISSN: None     Source Type: Journal    
DOI: 10.1216/rmjm/1181069830     Document Type: Article

References (21)

1. K. Balachandran, P. Balasubramaniam and J. P. Dauer, Controllability of nonlinear integrodifferential systems in Banach space, J. Optim. Theory Appl. 84 (1995), 83-91.
2. K. Balachandran, P. Balasubramaniam and J. P. Dauer, Local null controllability of nonlinear functional differential systems in Banach space, J. Optim. Theory Appl. 75 (1996), 61-75.
3. K. Balachandran, R. Sakthivel and J.P. Dauer, Controllability of neutral functional integrodifferential systems in Banach space, Comput. Math. Appl. 39 (2000), 117-126.
4. J. Banas and K. Goebel, Measures of noncompactness in Banach spaces, Marcel Dekker, New York, 1980.
5. M. Benchohra and S. K. Ntouyas, An existence result on noncompact intervals to first order integrodifferential inclusions in Banach spaces, Libertas Math. 20 (2000), 71-78.
6. M. Benchohra and S. K. Ntouyas, Controllability of nonlinear differential equations in Banach spaces with nonlocal conditions, J. Optim. Theory Appl. 110 (2001), 315-324.
7. M. Benchohra and S.K. Ntouyas, Controllability of nonlinear integrodifferential inclusions in Banach spaces with nonlocal conditions, Fasc. Math. 31 (2001), 5-22.
8. A. Bielecki, Une remarque sur la méthode de Banach-Cacciopoli-Tikhonov dans la theorie des equations differentielles ordinaires, Bull. Acad. Polon. Sci. 4 (1956), 261-264.
9. L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505.
10. L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problem, Select. Problems Math. 6 (1995), 25-33.
11. C. Castaing and M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Math., vol. 580, Springer-Verlag, Berlin, 1977.
12. H. Covitz and S.B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11.
13. K. Deimling, Multivalued differential equations, Walter de Gruyter, Berlin, 1992.
14. J.A. Goldstein, Semigroups of linear operators and applications, Oxford Univ. Press, New York, 1985.
15. L. Gorniewicz, Topological fixed point theory of multivalued mappings, Math. Appl., vol. 495, Kluwer Acad. Publ., Dordrecht, 1999.
16. Sh. Hu and N. Papageorgiou, Handbook of multivalued analysis, Vol. I: Theory, Kluwer Acad. Publ., Dordrecht, 1997.
17. A. Lasota and Z. Opial, An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
18. T.W. Ma, Topological degrees for set-valued compact vector fields in locally convex spaces, Dissertationes Math. 92, (1972), 1-43.
19. M. Martelli, A Rothe’s type theorem for non-compact acyclic-valued map, Boll. Un. Mat. Ital. 11 (1975), 70-76.
20. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983.
21. K. Yosida, Functional analysis, 6th ed., Springer-Verlag, Berlin, 1980.