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Existence of Solution, Filippov's Theorem and Compactness of the Set of Solutions for a Third-Order Differential Inclusion with Three- Point Boundary Conditions
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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
Mathematics (Basel), Vol.6(3), p.40
01/03/2018
DOI: https://doi.org/10.3390/math6030040

Abstract

Mathematics Physical Sciences Science & Technology
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.
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https://doi.org/10.3390/math6030040View
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