Existence results for semilinear neutral functional differential equations involving evolution operators in Fréchet spaces

Georgian Mathematical Journal

Volumn 17, Issue 3, 2010, Pages 423-436

  Baghli, Selma ^a   Benchohra, Mouffak ^a  

^a UNIVERSITY OF SIDI BEL ABBES   (Algeria)

Author keywords

Fixed point; Fr chet spaces; Mild solution; Nonlocal conditions; Semigroup; Semilinear neutral evolution equation

Indexed keywords

EID: 79960498929     PISSN: 1072947X     EISSN: 15729176     Source Type: Journal    
DOI: 10.1515/GMJ.2010.030     Document Type: Article

References (32)

1. S. G. Samko, On a progress in the theory of Lebesgue spaces with variable exponent:maximal and singular operators, Integral Transforms Spec. Funct., 16:5-6 (2005),461-482.
2. p. t/. OE0, (1) Mat. Zametki, 26:4(1979), 613-632 (Russian).
3. K. Stroethoff, Algebraic properties of Toeplitz operators on the Hardy space via the Berezin transform, in: Function spaces, (Edwardsville, IL, 1998), 313-319, Contemp. Math., 232, Amer. Math. Soc., Providence, RI, 1999.
4. K. Zhu, Operator Theory in Function Spaces, Monographs and Textbooks in Pureand Applied Mathematics, 139. Marcel Dekker, Inc., New York, 1990.
5. K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Graduate Texts in Mathematics,226. Springer-Verlag, New York, 2005.
6. K. Zhu, VMO, ESV, and Toeplitz operators on the Bergman space, Trans. Amer. Math. Soc., 302:2 (1987), 617-646.
7. K. Zhu, BMO and Hankel operators on Bergman spaces, Pacific J. Math., 155:2(1992), 377-395.
8. N. Zorboska, Toeplitz operators with BMO symbols and the Berezin transform, Int.J. Math. Math. Sci., 2003:46, 2929-2945.
9. K. Balachandran and R. R. Kumar, Existence of solutions of integrodifferential evolutionequations with time varying delays, Appl. Math. E-Notes, 7 (2007), 1-8 (electronic).
10. M. Benchohra, L. Górniewicz and S.K. Ntouyas, Controllability of neutral functionaldifferential and integrodifferential inclusions in Banach spaces with nonlocalconditions, Nonlinear Anal. Forum, 7 (2002), no. 1, 39-54.
11. M. Benchohra, L. Górniewicz and S.K. Ntouyas, Controllability of Some Nonlinear Systems in Banach spaces: The fixed Point Theory Approach, Pawel Wlodkowicz University College, Plock, 2003.
12. M. Benchohra and S. K. Ntouyas, Existence results on infinite intervals for neutralfunctional differential and integrodifferential inclusions in Banach spaces, Georgian Math. J., 7 (2000), no. 4, 609-625.
13. M. Benchohra and S. K. Ntouyas, Existence results for neutral functional differentialand integrodifferential inclusions in Banach spaces, Electron. J. Differential Equations2000, No. 20, 15 pp. (electronic).
14. M. Benchohra and S. K. Ntouyas, Controllability results for multivalued semilinearneutral functional equations, Math. Sci. Res. J., 6 (2002), no. 2, 65-77.
15. L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinearevolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162 (1991), no. 2,494-505.
16. L. Byszewski, Existence and uniqueness of solutions of semilinear evolution nonlocal Cauchy problem, Zeszyty Nauk. Politech. Rzeszowskiej Mat. Fiz., No. 18 (1993),109-112.
17. L. Byszewski, Existence and Uniqueness of Mild and Classical Solutions of Semilinear Functional-Differential Evolution Nonlocal Cauchy Problem, Selected problemsof mathematics, 25-33, 50th Anniv. Cracow Univ. Technol. Anniv. Issue, 6, Cracow Univ. Technol., Krakow, 1995.
18. L. Byszewski and H. Akca, On a mild solution of a semilinear functional-differentialevolution nonlocal problem, J. Appl. Math. Stochastic Anal., 10 (1997), no. 3, 265-271.
19. T. Cardinali and P. Rubbioni, On the existence of mild solutions of semilinear evolutiondifferential inclusions, J. Math. Anal. Appl., 308 (2005), no. 2, 620-635.
20. K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, ith contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli and R. Schnaubelt. Graduate Textsin Mathematics, 194. Springer-Verlag, New York, 2000.
21. M. Frigon and A. Granas, Résultats de type Leray-Schauder pour des contractionssur des espaces de Fréchet, (French) [Leray-Schauder-type results for contractionson Frechet spaces] Dedicated to the memory of Gilles Fournier (Sherbrooke, PQ,1997). Ann. Sci. Math. Québec, 22 (1998), no. 2, 161-168.
22. A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1969.
23. X. Fu, Controllability of neutral functional differential systems in abstract space, Appl. Math. Comput., 141 (2003), no. 2-3, 281-296.
24. X. Fu and K. Ezzinbi, Existence of solutions for neutral functional differential evolutionequations with nonlocal conditions, Nonlinear Anal., 54 (2003), no. 2, 215-227.
25. J. Hale, Theory of Functional Differential Equations, Second edition, Applied Mathematical Sciences, Vol. 3. Springer-Verlag, New York-Heidelberg, 1977.
26. J. K. Hale and S.M. Verduyn Lunel, Introduction to Functional-Differential Equations, Applied Mathematical Sciences, 99. Springer-Verlag, New York, 1993.
27. E. Hernandez M., AMassera type criterion for a partial neutral functional differentialequation, Electron. J. Differential Equations, 2002, No. 40, 17 pp.
28. M. Kamenskii, V. Obukhovskii and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, de Gruyter Series in Nonlinear Analysis and Applications, 7. Walter de Gruyter & Co., Berlin, 2001.
29. V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional-Differential Equations, Mathematics and its Applications, 463. Kluwer Academic Publishers, Dordrecht, 1999.
30. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44. Springer-Verlag, New York, 1983.
31. J. Wu, Theory and Applications of Partial Functional-Differential Equations, Applied Mathematical Sciences, 119. Springer-Verlag, New York, 1996.
32. K. Yosida, Functional Analysis, Sixth edition, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 123. Springer-Verlag, Berlin-New York, 1980.