Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-22T11:57:50.535Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological essentiality and differential inclusions

Published online by Cambridge University Press:  17 April 2009

Lech Gorniewicz  and
Miroslaw Slosarski
Lech Gorniewicz
Affiliation:
Institute of Mathematics University of NicholasCopernicus 87-100 Torun, Poland
Miroslaw Slosarski
Affiliation:
Institute of Mathematics University of NicholasCopernicus 87-100 Torun, Poland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the present paper a concept of topological essentiality for a large class of multivalued mappings is introduced. This concept is strictly related to the Leray-Schauder topological degree theory but is simpler and also more general. Applying the above concept to boundary value problems for differential inclusion with both upper semi-continuous and lower semi-continuous right hand sides, several new results are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 2 , April 1992 , pp. 177 - 193
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Aubin, J.P. and Cellina, A., Differential inclusions (Springer-Verlag, Berlin, Heidelberg, New York, 1984).CrossRefGoogle Scholar
[2]Bielawski, R. and Gorniewicz, L., Some applications of the Leray-Schauder alternative to differential equations, Editor Singh, S.P., pp. 187–194 (Reidel, 1986).Google Scholar
[3]Bressan, A. and Colombo, G., ‘Extensions and selections of maps with decomposable values’, Studia Math. 40 (1988), 69–86.CrossRefGoogle Scholar
[4]Frigon, M., ‘Application de la theorie de Ia transverssalite topologique a des problems non linearies pour des equations differentiales ordinaire’, Dissertationes Math, (to appear).Google Scholar
[5]Fryszkowski, A., ‘Existence of solutions of functional-differential inclusions in non-convex case’, Ann. Polon. Math. 45 (1985), 121–124.CrossRefGoogle Scholar
[6]Gorniewicz, L., ‘Homological methods in fixed point theory of multivalued mappings’, Dissertationes Math. 129 (1976), 1–71.Google Scholar
[7]Gorniewicz, L., ‘On the solution sets of differential inclusions’, J. Math. Anal. and Appl. 113 (1986), 235–244.CrossRefGoogle Scholar
[8]Gorniewicz, L., Granas, A. and Kryszewski, W., ‘Sur la methode de l’homotopie dans la theorie des points fixes pour les applications multivoques’, Transversalite topologique, C.R. Sci. Acad. Paris Ser 1 Math. 307 (1988), 489–492.Google Scholar
[9]Granas, A., ‘The theory of compact vector fields and some of its applications to topology of functional spaces’, Dissertationes Math. 30 (1962), 1–91.Google Scholar
[10]Granas, A., Guenther, R. and Lee, J., ‘Nonlinear boundary value problems for ordinary differential equations’, Dissertationes Math. 244 (1985), 1–130.Google Scholar
[11]Lze, J., Massabo, I., Pejsachowicz, J. and Vignoli, A., ‘Structure and dimension of global branches of solutions of multiparameter nonlinear equations’, Univ. National Aut. Mexico 350 (1983), 1–63.Google Scholar
[12]Kuratowski, K. and Ryll-Nardzewski, C., ‘A general theorem of selectors’, Bull. Acad. Polon Sci 6 (1965), 397–403.Google Scholar
[13]Lasry, M. and Robert, R., ‘Analyse nonlineaire multivoque’, Centre de Recherche de Math. de la Decision No. 7611, Univ. de Paris-Dauphine (1976).Google Scholar
[14]Pera, M.P., ‘A topological method for solving nonlinear equations in Banach spaces and some related global results on the structure of the solution sets’, Rend. Sem. Univ. Politec. Torino 41 (1983), 73–87.Google Scholar
[15]Pruszko, T., ‘Some applications of the topological degree theory to multivalued boundary value problems’, Dissertationes Math. 229 (1983), 1–52.Google Scholar