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ArticleOriginal scientific text

Title

Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory

Authors 1, 2

Affiliations

  1. Department of Mathematics, E.N.S., PoBox 92, 16050 Kouba, Algiers, Algeria
  2. Laboratory of Mathematics, Sidi-Bel-Abbès University, PoBox 89, 22000 Sidi-Bel-Abbès, Algeria

Abstract

In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are provided.

Keywords

ENG
differential inclusions, boundary value problem, fixed point, compact, convex, nonconvex, decomposable, continuous selection, controllability

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2010/30/1
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Pages:
23-49
Main language of publication
English
Received
2008-03-17
Accepted
2008-08-10
Published
2010

DOI: 10.7151/dmdico.1110

Exact and natural sciences