On solutions of the Volterra equation in the space of bounded variation functions
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Abstract
In this paper we use a Leray-Schauder alternative in order toprove the existence and uniqueness of solutions for the Volterra equation, with a initial condition, in the Banach space of the bounded variation functions.
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Matute, J.
(2014).
On solutions of the Volterra equation in the space of bounded variation functions.
Acta Mathematica Universitatis Comenianae, 83(2), 303-310.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/20/92
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References
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[2] Bugajeswska D., Bugajewski D. and Hudzik H., BV'-solutions of nonlinear integral equations, J. Math. Anal. Appl. 287 (2003) 265-278.
[3] Bugajewska D. and O0Regan D., On nonlinear integral equations and -bounded variation, Acta Math. Hung., 107 (4) (2005), 295-306.
[4] Bugajewski D., On BV-solutions of some nonlinear integral equations, Integr. Equa. Oper. Theory 46 (2003) 387-398.
[5] Chalishajar D. N. and George R. K., Exact controllability of generalized Hammerstein type integral equations and applications, Electronic Journal of Dierential Equations, Vol.
2006(2006), No. 142, pp.1-15.
[6] Federson M. and Bianconi R., Linear Volterra-Stieltjes integral equatios in the sense of the Kurzweil-Henstock integral, Archivum Mathematicum (BRNO), Tomus 37 (2001), 307-328.
[7] Hewitt E. and Stromberg K., Real and Abstract Analysis, Springer-Verlag, 1965.
[8] Josephy M., Composing functions of bounded variations, Proc. Amer. Math. Soc. 83 (1981), 354-356.
[9] Schwabik S., Tvrdy M. and Vejvoda O., Dierential and Integral Equations. Boundary value Problems and Adjoints, D. Reidel Publishing Co., DordrechtBoston, Mass.London, 1979.