Existence results for perturbed neutral functional evolution inclusions

L.G'orniewicz; S.K.Ntouyas

In this paper, we shall establish sufficient conditions for the existence of extremal mild solutions for perturbed neutral functional evolution inclusions in Banach spaces.

1. B.C. Dhage, A general multi-valued hybrid fixed point theorem and perurbed differential inclusions, Nonlinear Anal. 64 (2006), 2747-2772.

2. B.C. Dhage, E. Gatsori and S.K. Ntouyas, Existence theory for perturbed functional differential inclusions, Commun. Appl. Nonlinear Anal. 13 (2006), 1-14.

3. K. Deimling, Multivalued Differential Equations, De Gruyter, Berlin, 1992.

4. H. O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, North-Holland Mathematics Studies, Vol. 108, North-Holland, Amsterdam, 1985.

5. J.A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Univ. Press, New York, 1985.

6. L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999.

7. D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York, 1988.

8. S. Heikkila and V. Lakshmikantham, Monotone Iterative Technique for Nonlinear Discontinuous Differential Equations, Marcel Dekker Inc., New York, 1994.

9. E. Hernandez, Existence results for partial neutral functional integrodifferential equations with unbounded delay, J. Math. Anal. Appl. 292 (2004), 194--210.

10. Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer Academic Publishers, Dordrecht, 1997.

11. A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.

12. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.

13. C. Travis and G. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc. 200 (1974), 395--418.

14. C. Travis and G. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Hungarica 32 (1978), 75--96.

	Existence results for perturbed neutral functional evolution inclusions
Author	L.G'orniewicz, S.K.Ntouyas gorn@mat.uni.torun.pl, sntouyas@uoi.gr Schauder Center for Nonlinear Studies, Nicolaus Copernicus University,Chopina 12/18, 87-100 Torun, Poland, Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Abstract	In this paper, we shall establish sufficient conditions for the existence of extremal mild solutions for perturbed neutral functional evolution inclusions in Banach spaces.
Keywords	existence, perturbed neutral functional evelotion inclusion, Banach space, extremal mild solution
DOI	doi:10.30970/ms.28.1.57-70
Reference	1. B.C. Dhage, A general multi-valued hybrid fixed point theorem and perurbed differential inclusions, Nonlinear Anal. 64 (2006), 2747-2772. 2. B.C. Dhage, E. Gatsori and S.K. Ntouyas, Existence theory for perturbed functional differential inclusions, Commun. Appl. Nonlinear Anal. 13 (2006), 1-14. 3. K. Deimling, Multivalued Differential Equations, De Gruyter, Berlin, 1992. 4. H. O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, North-Holland Mathematics Studies, Vol. 108, North-Holland, Amsterdam, 1985. 5. J.A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Univ. Press, New York, 1985. 6. L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999. 7. D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York, 1988. 8. S. Heikkila and V. Lakshmikantham, Monotone Iterative Technique for Nonlinear Discontinuous Differential Equations, Marcel Dekker Inc., New York, 1994. 9. E. Hernandez, Existence results for partial neutral functional integrodifferential equations with unbounded delay, J. Math. Anal. Appl. 292 (2004), 194--210. 10. Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer Academic Publishers, Dordrecht, 1997. 11. A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786. 12. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. 13. C. Travis and G. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc. 200 (1974), 395--418. 14. C. Travis and G. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Hungarica 32 (1978), 75--96.
Pages	57-70
Volume	28
Issue	1
Year	2007
Journal	Matematychni Studii
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