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2012 | 10 | 6 | 2173-2186
Tytuł artykułu

Equivariant degree of convex-valued maps applied to set-valued BVP

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An equivariant degree is defined for equivariant completely continuous multivalued vector fields with compact convex values. Then it is applied to obtain a result on existence of solutions to a second order BVP for differential inclusions carrying some symmetries.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
6
Strony
2173-2186
Opis fizyczny
Daty
wydano
2012-12-01
online
2012-10-12
Twórcy
  • Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80-233, Gdańsk, Poland, zdzedzej@mif.pg.gda.pl
Bibliografia
  • [1] Antonyan S.A., Balanov Z.I., Gel’man B.D., Bourgin-Yang-type theorem for a-compact perturbations of closed operators. Part I. The case of index theories with dimension property, Abstr. Appl. Anal., 2006, #78928
  • [2] Balanov Z., Krawcewicz W., Rybicki S., Steinlein H., A short treatise on the equivariant degree theory and its applications, J. Fixed Point Theory Appl., 2010, 8(1), 1–74 http://dx.doi.org/10.1007/s11784-010-0033-9[Crossref][WoS]
  • [3] Balanov Z., Krawcewicz W., Steinlein H., Applied Equivariant Degree, AIMS Ser. Differ. Equ. Dyn. Syst., 1, American Institute of Mathematical Sciences, Springfield, 2006
  • [4] Borisovich Yu.G., Gel’man B.D., Myshkis A.D., Obukhovskii V.V., Introduction to the Theory of Multivalued Mappings and Differential Inclusions, URSS, Moscow, 2005 (in Russian)
  • [5] tom Dieck T., Transformation Groups, de Gruyter Stud. Math., 8, Walter de Gruyter, Berlin, 1987 http://dx.doi.org/10.1515/9783110858372[Crossref]
  • [6] Dzedzej Z., Kryszewski W., Selections and approximations of convex-valued equivariant mappings, Topol. Methods Nonlinear Anal. (in press)
  • [7] Erbe L.H., Krawcewicz W., Nonlinear boundary value problems for differential inclusions y″ ∈ F(t, y, y′), Ann. Polon. Math., 1991, 54(3), 195–226
  • [8] Górniewicz L., Topological Fixed Point Theory of Multivalued Mappings, Math. Appl., 495, Kluwer, Dordrecht-Boston-London, 1999
  • [9] Granas A., Guenther R., Lee J., Nonlinear Boundary Value Problems for Ordinary Differential Equations, Dissertationes Math. (Rozprawy Mat.), 244, Polish Academy of Sciences, Warsaw, 1985
  • [10] Hofmann K.H., Morris S.A., The Structure of Compact Groups, de Gruyter Stud. Math., 25, Walter de Gruyter, Berlin, 2006
  • [11] Krawcewicz W., Wu J., Theory of Degrees with Applications to Bifurcations and Differential Equations, Canad. Math. Soc. Ser. Monogr. Adv. Texts, John Wiley & Sons, New York, 1997
  • [12] Michael E., Continuous selections I, Annals of Math., 1956, 63(2), 361–382 http://dx.doi.org/10.2307/1969615[Crossref]
  • [13] Murayama M., On G-ANR’s and their G-homotopy types, Osaka J. Math., 1983, 20(3), 479–512
  • [14] Pruszko T., Topological degree methods in multivalued boundary value problems, Nonlinear Anal., 1981, 5(9), 959–973 http://dx.doi.org/10.1016/0362-546X(81)90056-0[Crossref]
  • [15] Pruszko T., Some Applications of the Topological Degree Theory to Multivalued Boundary Value Problems, Dissertationes Math. (Rozprawy Mat.), 229, Polish Academy of Sciences, Warsaw, 1984
  • [16] Rudin W., Functional Analysis, 2nd ed., Internat. Ser. Pure Appl. Math., McGraw-Hill, New York, 1991
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0099-2
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