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

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