Existence results for second-order impulsive neutral functional differential inclusions in Banach spaces

• Autorzy: Bahaj M. , Cherti I.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we investigate the existence of mild solutions on a compact interval to second-order impulsive neutral functional differential inclusions in Banach spaces. The results are obtained by using the theory of continuous cosine families and a fixed point theorem due to Dhage.

Słowa kluczowe

EN

impulsive neutral functional differential inclusions; fixed point theorem; existence theorem

PL

twierdzenie o punkcie stałym; twierdzenie o istnieniu

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2012
• Tom: Vol. 18, nr 2
• Strony: 225--242
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Bahaj M.

autor

Cherti I.

• Department of Mathematics, Faculty of Sciences & Technology, University Hassan I, 26000 Settat, Morocco,

Bibliografia

• [1] Z. Agur, L. Cojocaru, G. Mazaur, R. M. Anderson and Y. L. Danon, Pulse mass measles vaccination across age cohorts, Proc. Nat. Acad. Sci. USA 90 (1993), 11798-11702.
• [2] N. U. Ahmed, Systems governed by impulsive differential inclusions on Hilbert spaces, Nonlinear Anal. 45 (2001), 693-706.
• [3] M. Benchohra, J. Henderson and S. Ntouyas, Impulsive neutral functional differential equations in Banach spaces, Appl. Anal. 80 (2001), 353-365.
• [4] M. Benchohra, J. Henderson and S. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi, New York, 2006.
• [5] K. Deimling, Multivalued Differential Equations, de Gruyter Ser. Nonlinear Anal. Appl. 1, De Gruyter, Berlin, 1992.
• [6] B. C. Dhage, Multi-valued mappings and fixed points I, Nonlinear Func. Anal. Appl. 10 (2005), 359-378.
• [7] L. Erbe, H. I. Freedman, X. Z. Liu and J. H. Wu, Comparison principles for impulsive parabolic equations with applications to models of singles species growth, J. Austral. Math Soc. (B) 32 (1991), 382-400.
• [8] H. O. Fattorini, Ordinary differential equations in linear topological spaces. I, J. Differential Equations 5 (1969), 72-105.
• [9] H. O. Fattorini, Ordinary differential equations in linear topological spaces. II, J. Differential Equations 6 (1969), 50-70.
• [10] A. Goldbeter, Y. X. Li and G. Dupont, Pulsatile signalling in intercellular communication: Experimental and theoretical aspects, in: Mathematics Applied to Biology and Medicine, Wuerz Publishing, Winnipeg, (1993), 429-439.
• [11] S. Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis, vol. I, Mathematics and its Applications 419, Kluwer Academic Publishers, Dordrecht, 1997.
• [12] M. Kirane and Y. V. Rogovchenko, Comparison results for systems of impulse parabolic equations with applications to population dynamics, Nonlinear Anal. 28 (1997), 263-276.
• [13] V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
• [14] A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
• [15] X. Liu and S. Zhang, A cell population model described by impulsive PDEs - Existence and numerical approximation, Math. Applic. 36 (1998), 1-11.
• [16] S. Marshal, J. H. Kim Anthoni and J. P. Dauer, Existence of mild solutions of second-order neutral functional differential inclusions with nonlocal conditions in Banach spaces, Int. J. Math. Math. Sci. 22 (2002), 1133-1149.
• [17] R. H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Robert E. Krieger, Florida, 1987.
• [18] S. K. Ntouyas, Existence results for impulsive partial neutral functional differential inclusions, Electron. J. Differential Equations (2005), paper no. 30, 1-11.
• [19] A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
• [20] C. C. Travis and G. F. Webb, Compactness, regularity, and uniform continuity properties of strongly continuous cosine families, Houston J. Math. 3 (1977), 555-567.
• [21] C. C. Travis and G. F Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hung. 32 (1978), 75-96.
• [22] C. C. Travis and G. F Webb, Second order differential equations in Banach space, in: Nonlinear Equations in Abstract Spaces, Academic Press (1978), 331-361.
• [23] K. Yosida, Functional Analysis, 6th ed., Grundlehren Math. Wiss. 123, Springer, Berlin, 1980.