Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2008.48.1.001
Title & Authors
Second Order Impulsive Neutral Functional Differential Inclusions Liu, Yicheng; Li, Zhixiang;
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.
M. Benchohra, J. Henderson and S. K. Ntouyas, On second order multivalued impulsive functional differential inclusions in Banach spaces, Abstract and Applied Analysis, 6(2001), 369-380.
M. Benchohra, J. Henderson and S. K. Ntouyas, On first order impulsive differential inclusions with periodic boundary conditions, Dynam. Contin. Discrete Impuls. Systems, 9(2002), 417-428.
A. Bressan and G. Colombo, Existence and solutions of maps withdecomposable values, Studia Math., 90(1988), 69-86.
G. L. Cai, The existence of positive solution of impulse neutral delay differential equation, J. Sys. Sci. Math. Scis., 24(1)(2004), 102-109.(In Chinese)
C. Castaing and M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Math., Springer-Verlag, Berlin, 580(1977).
Y. K. Chang and W. T. Li, Existence results for second order impulsive differential inclusions, J. Math. Anal. Appl., 301(2005), 477-490.
M. Frigon, Theoremes 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(1995), 51-87.
V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, heory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
Y. Liu and Z. Li, Schaefer Type Theorem and Periodic Solutions of Evolution Equations, J. Math. Anal. Appl., 316(2006), 237-255.
Y. Liu, J. Wu and Z. Li, Multiple Solutions of Some Impulsive Three-point Boundary Value Problems, DCDIS Proceedings: Impulsive Dynamical Systems and Applications, 3(2005), 579-586.
M. Martelli, A Rothe's type theorem for noncompact acyclic-valued maps, Boll. Un. Mat. Ital., 11(1975), 70-76.
J. J. Nieto, Periodic boundary value problems for first-order impulsive ordinary differential equations, Nonlinear Anal., 51(2002), 1223-1232.
H. Schaefer, Uber die methode der a priori-Schranken, Math. Ann., 129(1955), 415-416.