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Existence theorems for a multivalued boundary value problem

Published online by Cambridge University Press:  17 April 2009

Salvatore A. Marano
Affiliation:
Dipartimento di Matematica CittàUniversitaria Viale A. Doria, 6 – 95125 Catania, Italy
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Abstract

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Let F be a multifunction from [a, b] × ℝn × ℝn into ℝn, with non-empty closed convex values. In this paper we prove that, under suitable assumptions, the multivalued boundary value problem

has at least one solution uW2, p([a, b], ℝn). Next we point out some particular cases.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Bernfeld, S.R. and Lakshmikantham, V., An introduction to nonlinear boundary value problems (Academic Press, New York, London, 1974).Google Scholar
[2]Cinquini, S., ‘Problemi di valori al contorno per equazioni differenziali (non lineari) del secondo ordine’, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2) 8 (1939), 122.Google Scholar
[3]Erbe, L.H. and Krawcewicz, W., ‘Boundary value problems for differential inclusions’, in Lecture Notes in Pure and Appl. Math. 127, pp. 115135 (Marcel Dekker, 1991).Google Scholar
[4]Frigon, M. and Granas, A., ‘Théorèmes d'existence pour des inclusions différentielles sans convexité’, C.R. Acad. Sci. Paris. Série I Math. 310 (1990), 819822.Google Scholar
[5]Granas, A., Guenther, R.B. and Lee, J.W., ‘Some existence results for the differential inclusions y (k)f(x, y,…, y(k−1)), yB’, C.R. Acad. Sci. Paris. Série I Math. 307 (1988), 391396.Google Scholar
[6]Hartman, P., Ordinary differential equations (John Wiley and Sons, New York, London, Sydney, 1964).Google Scholar
[7]Ricceri, O. Naselli and Ricceri, B., ‘An existence theorem for inclusions of the type ψ(u)(t) ∈ F(t, Φ(u)(t)) and application to a multivalued boundary value problem’, Appl. Anal. 38 (1990), 259270.CrossRefGoogle Scholar
[8]Pruszko, T., ‘Some applications of the topological degree theory to multi-valued boundary value problems’, in Dissertationes Math. 229, pp. 148, 1984.Google Scholar
[9]Dragoni, G. Scorza, ‘Elementi uniti di trasformazioni funzionali e problemi di valori ai limiti’, Rend. Sem. Mat. Univ. Roma (4) 2 (1938), 255275.Google Scholar
[10]Thompson, H.B., ‘Minimal solutions for two point boundary value problems’, Rend. Circ. Mat. Palermo (2) 37 (1988), 261281.CrossRefGoogle Scholar