Previous |  Up |  Next


Title: The periodic problem for semilinear differential inclusions in Banach spaces (English)
Author: Bader, Ralf
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 39
Issue: 4
Year: 1998
Pages: 671-684
Category: math
Summary: Sufficient conditions on the existence of periodic solutions for semilinear differential inclusions are given in general Banach space. In our approach we apply the technique of the translation operator along trajectories. Due to recent results it is possible to show that this operator is a so-called decomposable map and thus admissible for certain fixed point index theories for set-valued maps. Compactness conditions are formulated in terms of the Hausdorff measure of noncompactness. (English)
Keyword: periodic solutions
Keyword: translation operator along trajectories
Keyword: set-valued maps
Keyword: $C_0$-semigroup
Keyword: $R_\delta$-sets
MSC: 34A60
MSC: 34C25
MSC: 34G25
MSC: 47H11
MSC: 47N20
idZBL: Zbl 1060.34508
idMR: MR1715457
Date available: 2009-01-08T18:47:24Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Akhmerov R.R., Kamenskii M.I., Potapov A.S., Rodkina A.E., Sadovskii B.N.: Measures of Noncompactness and Condensing Operators.Birkhäuser Verlag, Basel-Boston-Berlin, 1992. MR 1153247
Reference: [2] Bader R.: Fixpunktindextheorie mengenwertiger Abbildungen und einige Anwendungen.Ph.D. Dissertation, Universität München, 1995. Zbl 0865.47049
Reference: [3] Bader R.: Fixed point theorems for compositions of set-valued maps with single-valued maps.submitted. Zbl 1012.47043
Reference: [4] Bader R., Kryszewski W.: Fixed-point index for compositions of set-valued maps with proximally $\infty$-connected values on arbitrary ANR's.Set-Valued Analysis 2 (1994), 459-480. Zbl 0846.55001, MR 1304049
Reference: [5] Bothe D.: Multivalued perturbations of $m$-accretive differential appear in Israel J. Math. Zbl 0922.47048, MR 1669396
Reference: [6] Conti G., Obukhovskii V., Zecca P.: On the topological structure of the solution set for a semilinear functional-differential inclusion in a Banach Topology in Nonlinear Analysis, K. Geba and L. Górniewicz (eds.), Polish Academy of Sciences, Institute of Mathematics, Banach Center Publications 35, Warszawa, 1996, pp.159-169. MR 1448435
Reference: [7] Deimling K.: Multivalued differential Gruyter, Berlin-New York, 1992. Zbl 0820.34009, MR 1189795
Reference: [8] Diestel J.: Geometry of Banach Spaces - Selected Topics.LNM 485, Springer-Verlag, Berlin-Heidelberg-New York, 1975. Zbl 0466.46021, MR 0461094
Reference: [9] Górniewicz L.: Topological approach to differential inclusions in: Topological methods in differential equations and inclusions, A. Granas and M. Frigon (eds.), NATO ASI Series C 472, Kluwer Academic Publishers, 1995, pp.129-190.. MR 1368672
Reference: [10] Hyman D.M.: On decreasing sequences of compact absolute retracts.Fund. Math. 64 (1969), 91-97. Zbl 0174.25804, MR 0253303
Reference: [11] Kamenskii M.I., Obukhovskii V.V.: Condensing multioperators and periodic solutions of parabolic functional-differential inclusions in Banach spaces.Nonlinear Anal. 20 (1993), 781-792. MR 1214743
Reference: [12] Kamenskii M., Obukhovskii V., Zecca P.: Condensing multivalued maps and semilinear differential inclusions in Banach in preparation. Zbl 0988.34001
Reference: [13] Kamenskii M., Obukhovskii V., Zecca P.: On the translation multioperator along the solutions of semilinear differential inclusions in Banach appear in Rocky Mountain J. Math. MR 1661823
Reference: [14] Krasnoselskii M.A.: The operator of translation along trajectories of differential equations.American Math. Soc., Translation of Math. Monographs, vol. 19, Providence, 1968. MR 0223640
Reference: [15] Lasota A., Opial Z.: Fixed-point theorems for multi-valued mappings and optimal control problems.Bull. Polish Acad. Sci. Math. 16 (1968), 645-649. Zbl 0165.43304, MR 0248580
Reference: [16] Mönch H., von Harten G.-F.: On the Cauchy problem for ordinary differential equations in Banach spaces.Archiv Math. 39 (1982), 153-160. MR 0675655
Reference: [17] Muresan M.: On a boundary value problem for quasi-linear differential inclusions of evolution.Collect. Math. 45 2 (1994), 165-175. Zbl 0824.34017, MR 1316934
Reference: [18] Papageorgiou N.S.: Boundary value problems for evolution inclusions.Comment. Math. Univ. Carolinae 29 (1988), 355-363. Zbl 0696.35074, MR 0957404
Reference: [19] Pazy A.: Semigroups of linear operators and applications to partial differential equations.Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1983. Zbl 0516.47023, MR 0710486


Files Size Format View
CommentatMathUnivCarolRetro_39-1998-4_4.pdf 244.6Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo