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Article

Cammaroto, Filippo ; Cubiotti, Paolo
Implicit integral equations with discontinuous right-hand side. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 38 (1997), issue 2, pp. 241-246
MSC: 45G10, 47H04, 47H15, 47N20 | MR 1455490 | Zbl 0886.47031
Keywords:
integral equations; discontinuity; bounded solutions
Summary:
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.
References:
[1] Aubin J.P., Cellina A.: Differential Inclusions. Springer-Verlag, Berlin, 1984. MR 0755330 | Zbl 0538.34007
[2] Aubin J.P., Frankowska H.: Set-Valued Analysis. Birkhäuser, Boston, 1990. MR 1048347 | Zbl 1168.49014
[3] Banas J., Knap Z.: Integrable solutions of a functional-integral equation. Rev. Mat. Univ. Complut. Madrid 2 (1989), 31-38. MR 1012104 | Zbl 0679.45003
[4] Emmanuele G.: About the existence of integrable solutions of a functional-integral equation. Rev. Mat. Univ. Complut. Madrid 4 (1991), 65-69. MR 1142550 | Zbl 0746.45004
[5] Emmanuele G.: Integrable solutions of a functional-integral equation. J. Integral Equations Appl. 4 (1992), 89-94. MR 1160090 | Zbl 0755.45005
[6] Fečkan M.: Nonnegative solutions of nonlinear integral equations. Comment. Math. Univ. Carolinae 36 (1995), 615-627. MR 1378685
[7] Hewitt E., Stromberg K.: Real and Abstract Analysis. Springer-Verlag, Berlin, 1965. MR 0367121 | Zbl 0307.28001
[8] Kantorovich L.V., Akilov G.P.: Functional Analysis in Normed Spaces. Pergamon Press, Oxford, 1964. MR 0213845 | Zbl 0127.06104
[9] Klein E., Thompson A.C.: Theory of Correspondences. John Wiley and Sons, New York, 1984. MR 0752692 | Zbl 0556.28012
[10] Lang S.: Real and Functional Analysis. Springer-Verlag, New York, 1993. MR 1216137 | Zbl 0831.46001
[11] 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. MR 1116184
[12] Ricceri B.: Sur la semi-continuité inférieure de certaines multifonctions. C.R. Acad. Sci. Paris, Série I 294 (1982), 265-267. MR 0653748 | Zbl 0483.54010
[13] Saint Raymond J.: Riemann-measurable selections. Set-Valued Anal. 2 (1994), 481-485. MR 1304050 | Zbl 0851.54021
[14] Villani A.: On Lusin's condition for the inverse function. Rend. Circ. Mat. Palermo 33 (1984), 331-335. MR 0779937 | Zbl 0562.26002
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