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Existence and controllability results for impulsive partial functional differential inclusions. (English) Zbl 1160.34068
Using fixed point arguments, the authors prove existence and controllability results for initial value problems for first order semilinear impulsive functional differential inclusions with multivalued jump operators, in a separable Banach space, with local and nonlocal conditions.

34K30Functional-differential equations in abstract spaces
34K05General theory of functional-differential equations
34K45Functional-differential equations with impulses
34K35Functional-differential equations connected with control problems
Full Text: DOI
[1] Ahmed, N. U.: Semigroup theory with applications to systems and control, Pitman research notes in mathematics series 246 (1991) · Zbl 0727.47026
[2] Ahmed, N. U.: Dynamic systems and control with applications, (2006) · Zbl 1127.93001
[3] Ahmed, N. U.: Systems governed by impulsive differential inclusions on Hilbert spaces, Nonlinear anal. 45, 693-706 (2001) · Zbl 0995.34053 · doi:10.1016/S0362-546X(99)00417-4
[4] Ahmed, N. U.: Optimal control for impulsive systems in Banach spaces, Int. J. Differ. equ. Appl. 1, No. 1, 37-52 (2000) · Zbl 0959.49023
[5] Balachandran, K.; Manimegalai, P.: Controllability of nonlinear abstract neutral evolution integrodifferential systems, Nonlinear funct. Anal. appl. 7, 85-100 (2002) · Zbl 0997.93012
[6] Bainov, D. D.; Simeonov, P. S.: Systems with impulsive effect, (1989) · Zbl 0671.34052
[7] Benchohra, M.; Gatsori, E. P.; Górniewicz, L.; Ntouyas, S. K.: Controllability results for evolution inclusions with non-local conditions, Z. anal. Anwendungen 22, 411-431 (2003) · Zbl 1052.34073 · doi:10.4171/ZAA/1153
[8] M. Benchohra, L. Górniewicz, S.K. Ntouyas, Controllability of Some Nonlinear Systems in Banach spaces: The Fixed Point Theory Approach, Pawel Wlodkowicz University College, Plock, 2003 · Zbl 1059.49001
[9] Benchohra, M.; Henderson, J.; Ntouyas, S. K.: Impulsive differential equations and inclusions, Impulsive differential equations and inclusions 2 (2006) · Zbl 1130.34003
[10] Benchohra, M.; Ntouyas, S. K.: Existence and controllability results for multivalued semilinear differential equations with nonlocal conditions, Soochow J. Math. 29, 157-170 (2003) · Zbl 1033.34068
[11] Benchohra, M.; Ntouyas, S. K.: Existence of mild solutions for certain delay semilinear evolution inclusions with nonlocal condition, Dynam. systems appl. 9, No. 3, 405-412 (2000) · Zbl 0974.34076
[12] Benchohra, M.; Ntouyas, S. K.: Nonlocal Cauchy problems for neutral functional differential and integrodifferential inclusions in Banach spaces, J. math. Anal. appl. 258, No. 2, 573-590 (2001) · Zbl 0982.45008 · doi:10.1006/jmaa.2000.7394
[13] Benchohra, M.; Ntouyas, S. K.: Existence of mild solutions of semilinear evolution inclusions with nonlocal conditions, Georgian math. J. 7, No. 2, 221-230 (2002) · Zbl 0960.34049
[14] Benedetti, I.: An existence result for impulsive functional differential inclusions in Banach spaces, Discuss. math. Differ. incl. Control optim. 24, 13-30 (2004) · Zbl 1071.34087
[15] Byszewski, L.: Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. math. Anal. appl. 162, 494-505 (1991) · Zbl 0748.34040 · doi:10.1016/0022-247X(91)90164-U
[16] Byszewski, L.: Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problems, Selected problems math. 6, 25-33 (1995)
[17] Byszewski, L.; Akca, H.: On a mild solution of a semilinear functional-differential evolution nonlocal problem, J. appl. Math. stoch. Anal. 10, 265-271 (1997) · Zbl 1043.34504 · doi:10.1155/S1048953397000336
[18] Deimling, K.: Multivalued differential equations, (1992) · Zbl 0760.34002
[19] Dhage, B. C.: Multivalued mappings and fixed points, Nonlinear funct. Anal. appl. 10, 359-378 (2005) · Zbl 1100.47040
[20] Dhage, B. C.: A fixed point theorem for multivalued mappings on ordered Banach spaces with applications, Panamer. math. J. 15, 15-34 (2005) · Zbl 1215.47039
[21] Dhage, B. C.; Gastori, E.; Ntouyas, S. K.: Existence theory for perturbed functional differential inclusions, Commun. appl. Nonlinear anal. 13, 1-14 (2006)
[22] Górniewicz, L.: Topological fixed point theory of multivalued mappings, Mathematics and its applications 495 (1999) · Zbl 0937.55001
[23] Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones, (1988) · Zbl 0661.47045
[24] Hale, J. K.; Lunel, S. M. Verduyn: Introduction to functional differential equations, Applied mathematical sciences 99 (1993) · Zbl 0787.34002
[25] Heikkila, S.; Lakshmikantham, V.: Monotone iterative technique for nonlinear discontinuous differential equations, (1994)
[26] Hu, Sh.; Papageorgiou, N.: Handbook of multivalued analysis, volume I: Theory, (1997) · Zbl 0887.47001
[27] M. Kamenskii, V. Obukhovskii, P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, in: de Gruyter Series in Nonlinear Analysis and Applications, Berlin, 2001 · Zbl 0988.34001
[28] Kisielewicz, M.: Differential inclusions and optimal control, (1991) · Zbl 0731.49001
[29] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[30] Lasota, A.; Opial, Z.: An application of the Kakutani--Ky Fan theorem in the theory of ordinary differential equations, Bull. acad. Pol sci. Ser. sci. Math. astronom. Phys. 13, 781-786 (1965) · Zbl 0151.10703
[31] Li, G.; Xue, X.: Controllability of evolution inclusions with nonlocal conditions, Appl. math. Comput. 141, 375-384 (2003) · Zbl 1029.93003 · doi:10.1016/S0096-3003(02)00262-X
[32] Migorski, S.; Ochal, A.: Nonlinear impulsive evolution inclusions of second order, Dynam. systems appl. 16, 155-173 (2007) · Zbl 1128.34038
[33] Pazy, A.: Semigroups of linear operators and applications to partial differential equations, (1983) · Zbl 0516.47023
[34] Quinn, M. D.; Carmichael, N.: An approach to nonlinear control problems using the fixed point methods, degree theory and pseudo-inverses, Numer. funct. Anal. optim. 7, 197-219 (1984--1985) · Zbl 0563.93013 · doi:10.1080/01630568508816189
[35] Rogovchenko, Yuri V.: Impulsive evolution systems: Main results and new trends, Dyn. contin. Discrete impuls. Syst. 3, No. 1, 57-88 (1997) · Zbl 0879.34014
[36] Rogovchenko, Yuri V.: Nonlinear impulsive evolution systems and applications to population models, J. math. Anal. appl. 207, No. 2, 300-315 (1997) · Zbl 0876.34011 · doi:10.1006/jmaa.1997.5245
[37] Samoilenko, A. M.; Perestyuk, N. A.: Impulsive differential equations, (1995) · Zbl 0837.34003
[38] Wu, J.: Theory and applications of partial functional differential equations, Applied mathematical sciences 119 (1996) · Zbl 0870.35116