Electron. J. Diff. Eqns., Vol. 2008(2008), No. 62, pp. 1-11.

On boundary-value problems for higher-order differential inclusions

Myelkebir Aitalioubrahim, Said Sajid

Abstract:
We show the existence of solutions to boundary-value problems for higher-order differential inclusion $x^{(n)}(t) \in F(t,x(t))$, where $F(.,.)$ is a closed multifunction, measurable in $t$ and Lipschitz continuous in $x$. We use the fixed point theorem introduced by Covitz and Nadler for contraction multivalued maps.

Submitted March 14, 2007. Published April 22, 2008.
Math Subject Classifications: 34A60, 34B10, 34B15.
Key Words: Boundary value problems; contraction; measurability; multifunction.

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Myelkebir Aitalioubrahim
University Hassan II-Mohammedia, U.F.R Mathematics and applications
F.S.T, B P 146, Mohammedia, Morocco
email: aitalifr@yahoo.fr
Said Sajid
University Hassan II-Mohammedia, U.F.R Mathematics and applications
F.S.T, B P 146, Mohammedia, Morocco
email: saidsajid@hotmail.com

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