Integral inclusions of upper semi-continuous or lower semi-continuous type

O’Regan, Donal

doi:10.1090/S0002-9939-96-03456-9

Integral inclusions of upper semi-continuous or lower semi-continuous type
HTML articles powered by AMS MathViewer

by Donal O’Regan PDF

Proc. Amer. Math. Soc. 124 (1996), 2391-2399 Request permission

Abstract:

Topological results for set valued maps are used to establish existence results for integral inclusions of Volterra or Hammerstein type.

References

Alberto Bressan and Giovanni Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), no. 1, 69–86. MR 947921, DOI 10.4064/sm-90-1-69-86
A. I. Bulgakov and L. N. Ljapin, Some properties of the set of solutions of a Volterra-Hammerstein integral inclusion, Differentsial′nye Uravneniya 14 (1978), no. 8, 1465–1472, 1532 (Russian). MR 507406
C. Corduneanu, Integral equations and applications, Cambridge University Press, Cambridge, 1991. MR 1109491, DOI 10.1017/CBO9780511569395
C. Corduneanu, Perturbation of linear abstract Volterra equations, J. Integral Equations Appl. 2 (1990), no. 3, 393–401. MR 1094476, DOI 10.1216/jiea/1181075570
James Dugundji and Andrzej Granas, Fixed point theory. I, Monografie Matematyczne [Mathematical Monographs], vol. 61, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1982. MR 660439
Marlène Frigon and Andrzej Granas, Théorèmes d’existence pour des inclusions différentielles sans convexité, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 12, 819–822 (French, with English summary). MR 1058503
G. Gripenberg, S.-O. Londen, and O. Staffans, Volterra integral and functional equations, Encyclopedia of Mathematics and its Applications, vol. 34, Cambridge University Press, Cambridge, 1990. MR 1050319, DOI 10.1017/CBO9780511662805
Donal O’Regan, Theory of singular boundary value problems, World Scientific Publishing Co., Inc., River Edge, NJ, 1994. MR 1286741, DOI 10.1142/9789814354097
—, Existence results for nonlinear integral equations, J. Math. Anal. Appl. 192 (1995), 705–726.
—, 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.
T. Pruszko, Topological degree methods in multivalued boundary value problems, J. Nonlinear Anal. 5 (1981), 953–973.
Tadeusz Pruszko, Some applications of the topological degree theory to multivalued boundary value problems, Dissertationes Math. (Rozprawy Mat.) 229 (1984), 48. MR 741752