Abstract
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.
[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 10.1155/AAA/2006/78928Search in Google Scholar
[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/s11784-010-0033-910.1007/s11784-010-0033-9Search in Google Scholar
[3] Balanov Z., Krawcewicz W., Steinlein H., Applied Equivariant Degree, AIMS Ser. Differ. Equ. Dyn. Syst., 1, American Institute of Mathematical Sciences, Springfield, 2006 Search in Google Scholar
[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) Search in Google Scholar
[5] tom Dieck T., Transformation Groups, de Gruyter Stud. Math., 8, Walter de Gruyter, Berlin, 1987 http://dx.doi.org/10.1515/978311085837210.1515/9783110858372Search in Google Scholar
[6] Dzedzej Z., Kryszewski W., Selections and approximations of convex-valued equivariant mappings, Topol. Methods Nonlinear Anal. (in press) Search in Google Scholar
[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 10.4064/ap-54-3-195-226Search in Google Scholar
[8] Górniewicz L., Topological Fixed Point Theory of Multivalued Mappings, Math. Appl., 495, Kluwer, Dordrecht-Boston-London, 1999 10.1007/978-94-015-9195-9Search in Google Scholar
[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 Search in Google Scholar
[10] Hofmann K.H., Morris S.A., The Structure of Compact Groups, de Gruyter Stud. Math., 25, Walter de Gruyter, Berlin, 2006 10.1515/9783110199772Search in Google Scholar
[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 Search in Google Scholar
[12] Michael E., Continuous selections I, Annals of Math., 1956, 63(2), 361–382 http://dx.doi.org/10.2307/196961510.2307/1969615Search in Google Scholar
[13] Murayama M., On G-ANR’s and their G-homotopy types, Osaka J. Math., 1983, 20(3), 479–512 Search in Google Scholar
[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)90056-010.1016/0362-546X(81)90056-0Search in Google Scholar
[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 Search in Google Scholar
[16] Rudin W., Functional Analysis, 2nd ed., Internat. Ser. Pure Appl. Math., McGraw-Hill, New York, 1991 Search in Google Scholar
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