Implicit integral equations with discontinuous right-hand side
Cammaroto, Filippo ; Cubiotti, Paolo
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 241-246 / Harvested from Czech Digital Mathematics Library
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We consider the integral equation $h(u(t))=f\big(\int_I g(t,x)\,u(x)\,dx\big)$, with $t\in[0,1]$, and prove an existence theorem for bounded solutions where $f$ is not assumed to be continuous.

Publié le : 1997-01-01
Classification:  45G10,  47H04,  47H15,  47N20 
@article{118921,
     author = {Filippo Cammaroto and Paolo Cubiotti},
     title = {Implicit integral equations with discontinuous right-hand side},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {241-246},
     zbl = {0886.47031},
     mrnumber = {1455490},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118921}
}

Cammaroto, Filippo; Cubiotti, Paolo. Implicit integral equations with discontinuous right-hand side. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 241-246. http://gdmltest.u-ga.fr/item/118921/

Aubin J.P.; Cellina A. Differential Inclusions, Springer-Verlag, Berlin, 1984. | MR 0755330 | Zbl 0538.34007

Aubin J.P.; Frankowska H. Set-Valued Analysis, Birkhäuser, Boston, 1990. | MR 1048347 | Zbl 1168.49014

Banas J.; Knap Z. Integrable solutions of a functional-integral equation, Rev. Mat. Univ. Complut. Madrid 2 (1989), 31-38. (1989) | MR 1012104 | Zbl 0679.45003

Emmanuele G. About the existence of integrable solutions of a functional-integral equation, Rev. Mat. Univ. Complut. Madrid 4 (1991), 65-69. (1991) | MR 1142550 | Zbl 0746.45004

Emmanuele G. Integrable solutions of a functional-integral equation, J. Integral Equations Appl. 4 (1992), 89-94. (1992) | MR 1160090 | Zbl 0755.45005

Fečkan M. Nonnegative solutions of nonlinear integral equations, Comment. Math. Univ. Carolinae 36 (1995), 615-627. (1995) | MR 1378685

Hewitt E.; Stromberg K. Real and Abstract Analysis, Springer-Verlag, Berlin, 1965. | MR 0367121 | Zbl 0307.28001

Kantorovich L.V.; Akilov G.P. Functional Analysis in Normed Spaces, Pergamon Press, Oxford, 1964. | MR 0213845 | Zbl 0127.06104

Klein E.; Thompson A.C. Theory of Correspondences, John Wiley and Sons, New York, 1984. | MR 0752692 | Zbl 0556.28012

Lang S. Real and Functional Analysis, Springer-Verlag, New York, 1993. | MR 1216137 | Zbl 0831.46001

Naselli Ricceri O.; Ricceri B. An existence theorem for inclusions of the type $\Psi(u)(t)\in F(t,\Phi(u)(t))$ and application to a multivalued boundary value problem, Appl. Anal. 38 (1990), 259-270. (1990) | MR 1116184

Ricceri B. Sur la semi-continuité inférieure de certaines multifonctions, C.R. Acad. Sci. Paris, Série I 294 (1982), 265-267. (1982) | MR 0653748 | Zbl 0483.54010

Saint Raymond J. Riemann-measurable selections, Set-Valued Anal. 2 (1994), 481-485. (1994) | MR 1304050 | Zbl 0851.54021

Villani A. On Lusin's condition for the inverse function, Rend. Circ. Mat. Palermo 33 (1984), 331-335. (1984) | MR 0779937 | Zbl 0562.26002