Nonlocal quasilinear damped differential inclusions

Electronic Journal of Differential Equations

Volumn 2002, Issue , 2002, Pages

  Benchohra, Mouffak ^a   Gatsori, Efrosini P ^b   Ntouyas, Sotiris K ^a  

^a UNIVERSITY OF SIDI BEL ABBES   (Algeria)

^b UNIVERSITY OF IOANNINA   (Greece)

Author keywords

Damped equations; Evolution inclusion; Fixed point; Initial value problems; Mild solution; Multivalued map; Nonlocal condition

Indexed keywords

EID: 3042528262     PISSN: 10726691     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. K. Balachandran and M. Chandrasekaran, Existence of solutions of a delay differential equation with nonlocal condition, Indian J. Pure Appl. Math. 27 (5) (1996), 443-449.
2. J. Banas and K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel-Dekker, New York, 1980.
3. L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional differential evolution nonlocal Cauchy problem, Selected Problems of Mathematics, Cracow Univ. of Tech., Aniversary Issue, 6 (1995), 25-33.
4. 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.
5. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, vol. 580, Springer-Verlag, BerlinHeidelberg-New York, 1977.
6. H. Covitz and S. B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11.
7. K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin-New York, 1992.
8. H. O. Fattorini, Second Order Ordinary differential equations in Banach spaces, North Holland, Amsterdam, 1985.
9. J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Univ. Press, New York, 1985.
10. L. Gorniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999.
11. S. Heikkila and V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, New York, 1994.
12. S. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer Academic Publishers, Dordrecht, Boston, London, 1997.
13. A. Lasota and Z. Opial, An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sei. Ser. Sei. Math. Astronom. Phys. 13 (1965), 781-786.
14. M. Martelli, A Rothe's type theorem for non-compact acyclic-valued map, Boll. Un. Mat. Hal. (4) 11 (1975), no 3. suppl., 70-76.
15. M. Matos and D. Pereira, On a hyperbolic equation with strong damping, Funkcial. Ekvac. 34 (1991), 303-311.
16. S. K. Ntouyas and P. Ch. Tsamatos, Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl. 210 (1997), 679-687.
17. S. K. Ntouyas and P. Ch. Tsamatos, Global existence for second order semilinear ordinary and delay integrodifferential equations with nonlocal conditions, Applic. Anal. 67 (1997), 245-257.
18. S. K. Ntouyas, Global existence results for certain second order delay integrodifferential equations with nonlocal conditions, Dynam. Systems Appl. 7 (1998), 415-426.
19. S. K. Patcheu, On the global solution and asymptotic behaviour for the generalized damped extensible beam equation, J. Differential Equations 135 (1997), 299-314.
20. C. C. Travis and G.F. Webb, Second order differential equations in Banach spaces, Proc. Int. Symp. on Nonlinear Equations in Abstract Spaces, Academic Press, New York (1978), 331-361.
21. C. C. Travis and G.F. Webb, Cosine families and abstract nonlinear second order differential equations, Ada Math. Hung. 32 (1978), 75-96.
22. K. Yosida, Functional Analysis, 6 edn. Springer-Verlag, Berlin, 1980.