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2011 | 31 | 1 | 39-69
Tytuł artykułu

Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator

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Języki publikacji
EN
Abstrakty
EN
We study a controllability problem for a system governed by a semilinear functional differential inclusion in a Banach space in the presence of impulse effects and delay. Assuming a regularity of the multivalued non-linearity in terms of the Hausdorff measure of noncompactness we do not require the compactness of the evolution operator generated by the linear part of inclusion. We find existence results for mild solutions of this problem under various growth conditions on the nonlinear part and on the jump functions. As example, we consider the controllability of an impulsive system governed by a wave equation with delayed feedback.
Twórcy
  • Università degli Studi di Firenze, Dipartimento di Energetica "S. Stecco", via S. Marta 3-1, 50139 Firenze, Italia
  • Voronezh State University, Faculty of Mathematics, Universitetskaya pl. 1, 394006 Voronezh, Russia
autor
  • Università degli Studi di Firenze, Dipartimento di Energetica "S. Stecco", via S. Marta 3-1, 50139 Firenze, Italia
Bibliografia
  • [1] N. Abada, M. Benchohra, H. Hammouche and A. Ouahab, Controllability of impulsive semilinear functional inclusions with finite delay in Fréchet spaces, Discuss. Math. Differ. Incl. Control Optim. 27 (2) (2007), 329-347. doi: 10.7151/dmdico.1088
  • [2] N. Abada, M. Benchohra and H. Hammouche, Existence and controllability results for impulsive partial functional differential inclusions, Nonlinear Analysis T.M.A. 69 (2008), 2892-2909. empty
  • [3] K. Balachandran and J.P. Dauer, Controllability of nonlinear systems in Banach spaces: a survey, J. Optim. Theory Appl. 115 (1) (2002), 7-28. doi: 10.1023/A:1019668728098
  • [4] M. Benchora, L. Górniewicz, S.K. Ntouyas and A. Ouahab, Controllability results for impulsive differential inclusions, Reports on Mathematical Physics 54 (2) (2004), 211-228. doi: 10.1016/S0034-4877(04)80015-6
  • [5] M. Benchohra, J. Henderson and S. Ntouyas, Impulsive Differential Equations and Inclusions, Contemporary Mathematics and Its Applications, 2. Hindawi Publishing Corporation, New York, 2006. doi: 10.1155/9789775945501
  • [6] I. Benedetti, An existence result for impulsive functional differential inclusions in Banach spaces, Discuss. Math. Diff. Incl. Contr. Optim. 24 (2004), 13-30. doi: 10.7151/dmdico.1049
  • [7] I. Benedetti and P. Rubbioni, Existence of solutions on compact and non-compact intervals for semilinear impulsive differential inclusions with delay, Topol. Methods Nonlinear Anal. 32 (2) (2008), 227-245.
  • [8] T. Cardinali and P. Rubbioni, On the existence of mild solutions of semilinear evolution differential inclusions, J. Math. Anal. Appl. 308 (2) (2005), 620-635. doi: 10.1016/j.jmaa.2004.11.049
  • [9] T. Cardinali and P. Rubbioni, Mild solutions for impulsive semilinear evolution differential inclusions, J. Appl. Funct. Anal. 1 (3) (2006), 303-325.
  • [10] T. Cardinali and P. Rubbioni, Impulsive semilinear differential inclusions: topological structure of the solutions set and solutions on non compact domains, Nonlinear Anal. T.M.A. (in press).
  • [11] Y.K. Chang, Controllability of impulsive functional differential inclusions with infinite delay in Banach spaces, J. Appl. Math. Comput. 25 (1-2) (2007), 137-154. doi: 10.1007/BF02832343
  • [12] K.J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Text in Mathematics, 194, Springer Verlag, New York, 2000.
  • [13] M. Kamenskii, V. Obukhovskii and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, De Gruyter Ser. Nonlinear Anal. Appl. 7, Walter de Gruyter, Berlin-New York, 2001. doi: 10.1515/9783110870893
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  • [15] W. Kryszewski and S. Plaskacz, Periodic solutions to impulsive differential inclusions with constraints, Nonlinear Anal. 65 (9) (2006), 1794-1804. empty
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  • [17] B. Liu, Controllability of impulsive neutral functional differential inclusions with infinite delay, Nonlinear Anal. 60 (8) (2005), 1533-1552. doi: 10.1016/j.na.2004.11.022
  • [18] V. Obukhovski and P. Zecca, Controllability for systems governed by semilinear differential inclusions in a Banach space with a non-compact semigroup, Nonlinear Anal. 70 (9) (2009), 3424-3436. doi: 10.1016/j.na.2008.05.009
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  • [121] R. Triggiani, A note on the lack of exact controllability for mild solutions in Banach spaces, SIAM J. Control Optim. 15 (3) (1977), 407-411. doi: 10.1137/0315028
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  • [123] W. Zhang and M. Fan, Periodicity in a generalized ecological competition system governed by impulsive differential equations with delays, Math. Comput. Modelling 39 (4-5) (2004), 479-493. doi: 10.1016/S0895-7177(04)90519-5
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Bibliografia
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