In this paper the Leray-Schauder nonlinear alternative for multivalued maps combined with the semigroup theory is used to investigate the existence of mild solutions for first order impulsive semilinear functional differential inclusions in Banach spaces.
@article{107859, author = {Mouffak Benchohra and Johnny Henderson and Sotiris K. Ntouyas}, title = {On first order impulsive semilinear functional differential inclusions}, journal = {Archivum Mathematicum}, volume = {039}, year = {2003}, pages = {129-139}, zbl = {1116.34342}, mrnumber = {1994569}, language = {en}, url = {http://dml.mathdoc.fr/item/107859} }
Benchohra, Mouffak; Henderson, Johnny; Ntouyas, Sotiris K. On first order impulsive semilinear functional differential inclusions. Archivum Mathematicum, Tome 039 (2003) pp. 129-139. http://gdmltest.u-ga.fr/item/107859/
Pulse mass measles vaccination across age cohorts, Proc. Nat. Acad. Sci. USA 90 (1993), 11698–11702.
Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980. | MR 0591679
Integral Equations and Applications, Cambridge Univ. Press, New York, 1990. | MR 1109491 | Zbl 1156.45001
Multivalued Differential Equations, De Gruyter, Berlin, 1992. | MR 1189795 | Zbl 0820.34009
Fixed Point Theory, Monografie Mat. PWN, Warsaw, 1982. | MR 0660439
Comparison principles for impulsive parabolic equations with applications to models of singles species growth, J. Austral. Math. Soc. Ser. B 32 (1991), 382–400. | MR 1097111
Pulsatile signalling in intercellular communication: Experimental and theoretical aspects, Mathematics applied to Biology and Medicine, Werz. Pub. Winnipeg, Canada (1993), 429–439.
Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, Boston, London, 1997. | MR 1485775
Comparison results for systems of impulsive parabolic equations with applications to population dynamics, Nonlinear Anal. 28 (1997), 263–276. | MR 1418135
Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. | MR 1082551
An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations, Bull. Polish Acad. Sci., Ser. Sci. Math. Astronom. Phys. 13 (1965), 781–786. | MR 0196178
Monotone iterative techniques for time-dependent problems with applications, J. Math. Anal. Appl. 237 (1999), 1–18. | MR 1708157
A cell population model described by impulsive PDEs-Existence and numerical approximation, Comput. Math. Appl. 36 (8) (1998), 1–11. | MR 1653819
A Rothe’s type theorem for non compact acyclic-valued maps, Boll. Un. Mat. Ital. 11 (Suppl. Fasc.) (1975), 70–76. | MR 0394752 | Zbl 0314.47035
Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. | MR 0710486 | Zbl 0516.47023
Impulsive Differential Equations, World Scientific, Singapore, 1995. | MR 1355787
Functional Analysis, $6^{\text{th}}$ edn. Springer-Verlag, Berlin, 1980. | MR 0617913 | Zbl 0830.46001