Second Order Impulsive Neutral Functional Differential Inclusions
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In this paper, we investigate the existence of solutions of second order impulsive neutral functional differential inclusions which the nonlinearity F admits convex and non-convex values. Some results under weaker conditions are presented. Our results extend previous ones. The methods rely on a fixed point theorem for condensing multivalued maps and Schaefer’s fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values.
Abstract
In this paper, we investigate the existence of solutions of second order impulsive neutral functional differential inclusions which the nonlinearity F admits convex and non-convex values. Some results under weaker conditions are presented. Our results extend previous ones. The methods rely on a fixed point theorem for condensing multivalued maps and Schaefer’s fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values.
참고문헌 (13)
- M. Benchohra, "Ntouyas, On second order multivalued impulsive functional differential inclusions in Banach spaces", Abstract and Applied Analysis, 6, pp.369~380 (2001)
- M. Benchohra, "On first order impulsive differential inclusions with periodic boundary conditions", Dynam. Contin. Discrete Impuls. Systems, 9, pp.417~428 (2002)
- A. Bressan, "Colombo, Existence and solutions of maps withdecomposable values", Studia Math, 90, pp.69~86 (1988)
- G. L. Cai, "The existence of positive solution of impulse neutral delay differential equation .(In Chinese)", J. Sys. Sci. Math. Scis, 24(1), pp.102~109 (2004)
- C. Castaing, "Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Math", Springer-Verlag Berlin, 580 (1977)
- Y. K. Chang, "Existence results for second order impulsive differential inclusions", J. Math. Anal. Appl, 301, pp.477~490 (2005)
- M. Frigon, "Theor`emes d'existence de solutions d'inclusions differentielles, Topological Methods in Differential Equations and Inclusions (edited by A. Granas and M. Frigon), NATO ASI Series C", Kluwer Acad. Publ, 472, pp.51~87 (1995)
- V. Lakshmikantham, "Simeonov, heory of Impulsive Differential Equations" (1989), World Scientific, Singapore
- Y. Liu, "Schaefer Type Theorem and Periodic Solutions of Evolution Equations", J. Math. Anal. Appl, 316, pp.237~255 (2006)
- Y. Liu, "Multiple Solutions of Some Impulsive Three-point Boundary Value Problems", DCDIS Proceedings: Impulsive Dynamical Systems and Applications, pp.579~586 (2005)
- M. Martelli, "A Rothe's type theorem for noncompact acyclic-valued maps", Boll. Un. Mat. Ital, 11, pp.70~76 (1975)
- J. J. Nieto, "Periodic boundary value problems for first-order impulsive ordinary differential equations", Nonlinear Anal, 51, pp.1223~1232 (2002)
- H. Schaefer, "Uber die methode der a priori-Schranken", Math. Ann, 129, pp.415~416 (1955)