Existence of Solution, Filippov’s Theorem and Compactness of the Set of Solutions for a Third-Order Differential Inclusion with Three- Point Boundary Conditions

Ali Rezaiguia and Smail Kelaiaia
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Ali Rezaiguia: Department of Mathematics and Computer Science, Faculty of Sciences , University of Souk Ahras, Souk Ahras 41000, Algeria
Smail Kelaiaia: Department of Mathematics, Faculty of Sciences, University of Annaba, P.O. Box 12, Annaba 23000, Algerie

Mathematics, 2018, vol. 6, issue 3, 1-12

Abstract: In this paper, we study a third-order differential inclusion with three-point boundary conditions. We prove the existence of a solution under convexity conditions on the multi-valued right-hand side; the proof is based on a nonlinear alternative of Leray-Schauder type. We also study the compactness of the set of solutions and establish some Filippov’s- type results for this problem.

Keywords: differential inclusion; boundary value problem; fixed point theorem; selection theory; Filippov’s Theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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