Integral inclusions of upper semi-continuous
or lower semi-continuous type
Author:
Donal O'Regan
Journal:
Proc. Amer. Math. Soc. 124 (1996), 2391-2399
MSC (1991):
Primary 45D05, 45G10
DOI:
https://doi.org/10.1090/S0002-9939-96-03456-9
MathSciNet review:
1342037
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Abstract | References | Similar Articles | Additional Information
Abstract: Topological results for set valued maps are used to establish existence results for integral inclusions of Volterra or Hammerstein type.
- 1. A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 70--85. MR 89j:54021
- 2. A. I. Bulgakov and L. N. Lyapin, Some properties of the set of solutions for the Volterra-Hammerstein integral inclusion, Differential Equations (Transl.) 14 (1978), 1043--1048. MR 80a:45007
- 3. C. Corduneanu, Integral equations and applications, Cambridge Univ. Press, New York, 1991. MR 92h:45001
- 4. ------, Perturbations of linear abstract Volterra equations, J. Internat. Eq. Appl. 2 (1990), 393--401. MR 92a:45005
- 5. J. Dugundji and A. Granas, Fixed point theory, Monografie Mathematyczne, PWN, Warsaw, 1982. MR 83j:54038
- 6. M. Frigon and A. Granas, Théorèmes d'existence pour des inclusions différentielles sans convexité, C.R. Acad. Sci. Paris, Ser. I 310 (1990), 819--822. MR 91e:34014
- 7. G. Gripenberg, S. O. Londen, and O. Staffans, Volterra integral and functional equations, Cambridge Univ. Press, New York, 1990. MR 91c:45003
- 8. D. O'Regan, Theory of singular boundary value problems, World Scientific Press, Singapore, 1994. MR 95g:34003
- 9. ------, Existence results for nonlinear integral equations, J. Math. Anal. Appl. 192 (1995), 705--726. CMP 95:14
- 10. ------, Existence theory for nonlinear Volterra and Hammerstein integral equations, Dynamical Systems and Applications (R. P. Agarwal, ed.), World Scientific Series in Applicable Analysis, Vol. 4 (1995), 601--615.
- 11. T. Pruszko, Topological degree methods in multivalued boundary value problems, J. Nonlinear Anal. 5 (1981), 953--973.
- 12. ------, Some applications of the topological degree theory to multivalued boundary value problems, Dissertationes Math. 229 (1984). MR 85j:34030
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Additional Information
Donal O'Regan
Affiliation:
Department of Mathematics, University College Galway, Galway, Ireland
Email:
donal.oregan@ucg.ie
DOI:
https://doi.org/10.1090/S0002-9939-96-03456-9
Received by editor(s):
February 6, 1995
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1996
American Mathematical Society