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Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces

Abada NadjatBenchohra MouffakHammouche HaddaOuahab Abdelghani — 2007

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space.

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

Smaïl DjebaliAbdelghani Ouahab — 2010

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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...

System of boundary random fractional differential equations via Hadamard derivative

Zakaria MalkiFarida BerhounAbdelghani Ouahab — 2021

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

We study the existence of solutions for random system of fractional differential equations with boundary nonlocal initial conditions. Our approach is based on random fixed point principles of Schaefer and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.

Existence results for boundary value problems for fourth-order differential inclusions with nonconvex valued right hand side

A. AraraMouffak BenchohraSotiris K. NtouyasAbdelghani Ouahab — 2004

Archivum Mathematicum

In this paper a fixed point theorem due to Covitz and Nadler for contraction multivalued maps, and the Schaefer’s theorem combined with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued operators with decomposables values, are used to investigate the existence of solutions for boundary value problems of fourth-order differential inclusions.

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