Opuscula Math. 32, no. 2 (2012), 205-226
http://dx.doi.org/10.7494/OpMath.2012.32.2.205

Opuscula Mathematica

# Boundary value problems for n-th order differential inclusions with four-point integral boundary conditions

Sotiris K. Ntouyas

Abstract. In this paper, we discuss the existence of solutions for a four-point integral boundary value problem of $$n$$-th order differential inclusions involving convex and non-convex multivalued maps. The existence results are obtained by applying the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.

Keywords: differential inclusions, four-point integral boundary conditions, existence, nonlinear alternative of Leray Schauder type, fixed point theorems.

Mathematics Subject Classification: 34A60, 34B10, 34B15.

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• King Abdulaziz University, Faculty of Science, Department of Mathematics, P.O. Box 80203, Jeddah 21589, Saudi Arabia
• Sotiris K. Ntouyas
• University of Ioannina, Department of Mathematics, 451 10 Ioannina, Greece
• Revised: 2011-04-06.
• Accepted: 2011-04-07.