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2006 | 26 | 1 | 143-158
Tytuł artykułu

Representation of the set of mild solutions to the relaxed semilinear differential inclusion

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Abstrakty
EN
We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.
Twórcy
  • Dipartimento di Energetica "S. Stecco", University of Florence, Via S. Marta 3, Firenze, Italy
  • Department of Mathematics, Physics, and Computer Science, Tambov State University, Internazional'naya str. 33, Tambov, Russia
Bibliografia
  • [1] J.-P. Aubin and A. Cellina, Differential Inclusions, Grundlehren Math. Wiss. Vol. 264, Springer-Verlag, Berlin, Heidelberg 1984.
  • [2] J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston-Basel-Berlin 1990.
  • [3] Yu. Borisovich, B. Gelman, A. Myshkis and V. Obukhovskii, Introduction to the Theory of Multivalued Maps and Differential Inclusions, Editorial URSS, Moscow 2005 (in Russian).
  • [4] A. Bulgakov, A. Efremov and E. Panasenko, Ordinary Differential Inclusions with Internal and External Perturbations, Differentsial'nye Uravneniya 36 (12) (2000), 1587-1598, translated in Differential Equations 36 (12) (2000), 1741-1753.
  • [5] K. Deimling, Multivalued Differential Equations, De Gruyter Sr. Nonlinear Anal. Appl. 1, Walter de Gruyter, Berlin-New York 1992.
  • [6] A.F. Filippov, Differential Equations with Discontinuous Righthand Side, Dordrecht, Kluwer 1988.
  • [7] H. Frankowska, A Priori Estimanes for Operational Differential Inclusions, J. Differential Equations 84 (1990), 100-128.
  • [8] A.D. Ioffe and V.M. Tihomirov, Theory of Extremal Problems, North Holland, Amsterdam 1979.
  • [9] M. Kamenskii, V. Obukhovskii and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, De Gruyter Sr. Nonlinear Anal. Appl. 7, Walter de Gruyter, Berlin-New York 2001.
  • [10] K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New-York, Inc. 2000.
  • [11] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New-York, Inc. 1983.
  • [12] G. Pianigiani, On the Fundamental Theory of Multivalued Differential Equations, J. Differential Equations 25 (1) (1977), 30-38.
  • [13] A. Plis, On Trajectories of Orientor Fields, Bull. Acad. Polon. Sci, Ser. Math. 13 (8) (1965) 571-573.
  • [14] A.A. Tolstonogov, Differential Inclusions in Banach Space, Kluwer Acad. Publishers, Dordrecht 2000.
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1071
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