Multivalued evolution equations with nonlocal initial conditions in Banach spaces

Nonlinear Differential Equations and Applications

Volumn 14, Issue 3-4, 2007, Pages 361-376

  Aizicovici, Sergiu ^a   Staicu, Vasile ^b  

^a OHIO UNIVERSITY   (United States)

^b UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Compact semigroup; Evolution inclusion; M accretive operator; Multifunction; Nonlocal Cauchy problem

Indexed keywords

EID: 38849123682     PISSN: 10219722     EISSN: 14209004     Source Type: Journal    
DOI: 10.1007/s00030-007-5049-5     Document Type: Article

References (28)

1. N. U. AHMED, Differential inclusions on Banach spaces with nonlocal state constraints, Nonlinear Funct. Anal. Appl. 16 (2001), 359-409.
2. S. AIZICOVICI and Y. GAO, Functional differential equations with nonlocal initial conditions, J. Appl. Math. Stochastic Anal. 10 (1997), 145-156.
3. S. AIZICOVICI and H. LEE, Nonlinear nonlocal Cauchy problems in Banach spaces, Appl. Math. Letters 18 (2005), 401-407.
4. S. AIZICOVICI and M. MCKIBBEN, Existence results for a class of abstract nonlocal Cauchy problems, Nonlinear Anal. 39 (2000), 649-668.
5. J. P. AUBIN and A. CELLINA, Differential Inclusions, Springer, Berlin, 1984.
6. J. P. AUBIN and H. FRANKOWSKA, Set-Valued Analysis, Birkhauser, Boston, 1990.
7. P. BARAS, Compacité de l'opérateur f → u solution d'une équation nonlinéaire (du/dt) +Au ∋ f, C. R. Acad. Sci. Paris 286 (1978), 1113-1116.
8. V. BARBU, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publ., Leyden, 1976.
9. M. BENCHOCHRA, E. GATSORI and S. K. NTOUYAS, Existence results for semi-linear integro-differential inclusions with nonlocal conditions, Rocky Mountain J. Math. 34 (2004), 833-848.
10. M. BENCHOCHRA, E. GATSORI and S. K. NTOUYAS, Multivalued semilinear neutral functional differential equations with nonconvex-valued righthand side, Abstr. Appl. Anal. 6 (2004), 525-541.
11. M. BENCHOHRA, Nonlocal Cauchy problems for neutral functional differential and integrodifferential inclusions in Banach spaces, J. Math. Anal. Appl. 258 (2001), 573-590.
12. P. BÉNILAN, Solutions integrales d'équations d'évolution dans un espace de Banach, C. R. Acad. Sci. Paris 274 (1972), 47-50.
13. A. BOUCHERIF, Nonlocal Cauchy problems for first order multivalued differential equations, Electron. J. Differential Equations 47 (2002), 1-9.
14. H. BRÉZIS, Opérateurs Maximaux Monotones et Semigroupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam, 1973.
15. 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.
16. R. CASCAVAL and I. I. VRABIE, Existence of periodic solutions for a class of nonlinear evolution equations, Rev. Mat. Complut. 7 (1994), 325-338.
17. M. CRANDALL and T. LIGGETT, Generation of semigroups of nonlinear transformations in Banach spaces, Amer. J. Math. 93 (1971), 265-298.
18. J. DIESTEL and J. UHL, Vector Measures, Amer. Math. Soc., Providence, R.I., 1977.
19. N. DUNFORD and J. T. SCHWARTZ, Linear Operators, Part I, Interscience, New York, 1958.
20. K. FAN, Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 121-126.
21. E. GATSORI, S. K. NTOUYAS and Y. G. SFICAS, On a nonlocal Cauchy problem for differential inclusions, Abstr. Appl. Anal. 5 (2004), 425-434.
22. S. HU and N. S. PAPAGEORGIOU, Handbook of Multivalued Analysis, Vol. I: Theory, Kluwer, Dordrecht, 1997.
23. S. HU and N. S. PAPAGEORGIOU, Handbook of Multivalued Analysis, Vol. II: Applications, Kluwer, Dordrecht, 2000.
24. A. G. KARTSATOS and K. Y. SHIN, Solvability of functional evolutions via compactness methods in general Banach spaces, Nonlinear Anal. 21 (1993), 517-535.
25. M. KISIELEWICZ, Differential Inclusions and Optimal Control, PWN-Polish Scientific Publishers and Kluwer Academic Publishers, Warszawa and Dordrecht, 1991.
26. N. H. PAVEL, Nonlinear Evolution Operators and Semigroups, Lecture Notes in Math. 1260, Springer, Berlin, 1987.
27. I. I. VRABIE, Compactness Methods for Nonlinear Evolutions, Longman, Harlow, 1987.
28. X. XUE, Nonlinear differential equations with nonlocal conditions in Banach spaces, Nonlinear Anal., 63 (2005), 575-586.