Abstract
The existence of solutions on a compact interval to second-order impulsive functional differential inclusions is investigated. Several new results are obtained by using Sadovskii's fixed point theorem.
The existence of solutions on a compact interval to second-order impulsive functional differential inclusions is investigated. Several new results are obtained by using Sadovskii's fixed point theorem.
M. Benchohra and A. Boucherif, “On first order initial value problems for impulsive differential inclusions in Banach spaces,” Dynamic Systems and Applications, vol. 8, no. 1, pp. 119–126, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Benchohra and A. Boucherif, “Initial value problems for impulsive differential inclusions of first order,” Differential Equations and Dynamical Systems, vol. 8, no. 1, pp. 51–66, 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Benchohra, J. Henderson, and S. K. Ntouyas, “On second-order multivalued impulsive functional differential inclusions in Banach spaces,” Abstract and Applied Analysis, vol. 6, no. 6, pp. 369–380, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Benchohra, J. Henderson, and S. K. Ntouyas, “On first order impulsive differential inclusions with periodic boundary conditions,” Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis, vol. 9, no. 3, pp. 417–427, 2002.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Benchohra, J. Henderson, and S. K. Ntouyas, “On first order impulsive semilinear functional differential inclusions,” Archivum Mathematicum (Brno), vol. 39, no. 2, pp. 129–139, 2003.
View at: Google Scholar | MathSciNetM. Benchohra and S. K. Ntouyas, “Initial and boundary value problems for nonconvex valued multivalued functional differential equations,” Journal of Applied Mathematics and Stochastic Analysis, vol. 16, no. 2, pp. 191–200, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Benchohra and A. Ouahab, “Impulsive neutral functional differential inclusions with variable times,” Electronic Journal of Differential Equations, vol. 2003, no. 67, pp. 1–12, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Bressan and G. Colombo, “Extensions and selections of maps with decomposable values,” Studia Mathematica, vol. 90, no. 1, pp. 69–86, 1988.
View at: Google Scholar | Zentralblatt MATH | MathSciNetY.-K. Chang and W.-T. Li, “Existence results for second order impulsive functional differential inclusions,” Journal of Mathematical Analysis and Applications, vol. 301, no. 2, pp. 477–490, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Deimling, Multivalued Differential Equations, vol. 1 of de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, 1992.
View at: MathSciNetM. Frigon, “Théorèmes d'existence de solutions d'inclusions différentielles,” in Topological Methods in Differential Equations and Inclusions (Montreal, PQ, 1994), A. Granas and M. Frigon, Eds., vol. 472 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pp. 51–87, Kluwer Academic, Dordrecht, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Frigon and D. O'Regan, “Boundary value problems for second order impulsive differential equations using set-valued maps,” Applicable Analysis, vol. 58, no. 3-4, pp. 325–333, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Hu and N. Papageorgiou, Handbook of Multivalued Analysis. Vol. I. Theory, vol. 419 of Mathematics and Its Applications, Kluwer Academic, Dordrecht, 1997.
View at: Zentralblatt MATH | MathSciNetV. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, New Jersey, 1989.
View at: Zentralblatt MATH | MathSciNetB. N. Sadovskii, “On a fixed point principle,” Functional Analysis and Its Applications, vol. 1, no. 2, pp. 74–76, 1967.
View at: Google Scholar | MathSciNet