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Nonlinear alternatives for multivalued maps
with applications to operator inclusions
in abstract spaces


Author: Donal O'Regan
Journal: Proc. Amer. Math. Soc. 127 (1999), 3557-3564
MSC (1991): Primary 47H10, 54C60, 54H25
DOI: https://doi.org/10.1090/S0002-9939-99-04949-7
Published electronically: May 13, 1999
MathSciNet review: 1610765
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Abstract: A nonlinear alternative of Leray-Schauder type is presented for condensing operators with closed graph. We will then use this theorem to establish new existence principles for differential and integral inclusions in Banach spaces.


References [Enhancements On Off] (What's this?)

  • [1] C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis, Springer Verlag, Berlin, 1994. MR 96k:46001
  • [2] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985. MR 86j:47001
  • [3] K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin, 1992. MR 94b:34026
  • [4] P.M. Fitzpatrick and W.V. Petryshyn, Fixed point theorems for multivalued noncompact acyclic mappings, Pacific Jour. Math., 54(1974), 17-23. MR 53:8973
  • [5] M. Frigon, Théoremes d'existence de solutions d'inclusions différentielles, Topological Methods in Differential Equations and Inclusions (edited by A. Granas and M. Frigon), NATO ASI Series C, Vol 472, Kluwer Acad. Publ., Dordrecht, 1995, 51-87. MR 96m:34025
  • [6] H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal., 4(1980), 985-999. MR 82c:34075
  • [7] D.O'Regan, A topological approach to integral inclusions, Proc. Royal Irish Acad., 97A(1997), 101-111.
  • [8] D.O'Regan, Abstract operator inclusions, Functional Differential Equations, 4(1-2)(1997), 143-154. CMP 98:07
  • [9] D.O'Regan, Multivalued integral equations in finite or infinite dimensions, Communications in Applied Analysis, 2(4)(1998), 487-496. CMP 98:16
  • [10] C.H. Su and V.M. Sehgal, Some fixed point theorems for condensing multifunctions in locally convex spaces, Proc. Amer. Math. Soc., 50(1975), 150-154. MR 52:1430

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Additional Information

Donal O'Regan
Affiliation: Department of Mathematics, National University of Ireland, Galway, Ireland
Email: donal.oregan@nuigalway.ie

DOI: https://doi.org/10.1090/S0002-9939-99-04949-7
Received by editor(s): September 10, 1997
Received by editor(s) in revised form: February 13, 1998
Published electronically: May 13, 1999
Communicated by: Dale Alspach
Article copyright: © Copyright 1999 American Mathematical Society

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