Abstract
This paper discusses the topological structure of the solution set of a general Volterra integral equation. Under natural conditions we show that the solution set is an \(R_{\delta}\) set.
Authors
Donal O’Regan
Department of Mathematics, National University of Ireland Galway, Ireland
Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Volterra integral equation; solution set; \(R_{\delta}\) set.
Paper coordinates
D. O’Regan, R. Precup, Aronszajn type theorems for integral equations on unbounded domains via maximal solutions, Fixed Point Theory, 4 (2006) no. 2, 305-313.
About this paper
Journal
Fixed Point Theory
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DOI
http://www.math.ubbcluj.ro/~nodeacj/vol__7(2006)_no_2.htm
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[1] R.P. Agarwal, L. Gorniewicz, D. O’Regan, Aronszajn type results for Volterra equations and inclusions, Topological Methods in Nonlinear Analysis, 23(2004), 149-159.
[2] R.P. Agarwal, M. Meehan, D. O’Regan, Nonlinear integral equations and inclusions, Nova Science Publishers, Huntington, New York, 2001.
[3] R.P. Agarwal, D. O’Regan, On the topological structure of fixed point sets for abstract Volterra operators on Frechet spaces, Jour. Nonlinear and Convex Analysis, 3(2000), 271-286.
[4] D.M. Bedivan, D. O’Regan, Fixed point sets for abstract Volterra operators on Frechet spaces, Applicable Analysis, 76(2000), 131-152.
[5] C. Corduneanu, Integral Equations and Applications, Cambridge University Press, Cambridge, 1991.
[6] Z. Kubacek, On the structure of fixed point sets of some compact maps in the Frechet space, Mathematica Bohemica, 118(1993), 343-358.
[7] V. Lakshmikantham, S. Leela, Differential and Integral Inequalities, Vol. I, Academic Press, New York, 1969.
[8] D. O’Regan, Topological structure of solution sets in Frechet spaces: the projective limit approach, Jour. Math. Anal. Appl., to appear.