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Omar Benslimane

Publications and source records attributed to Omar Benslimane.

5 recordsLinked to original sources
arXiv2023

Comments on "Necessary optimality conditions of an optimization problem governed by a double phase PDE"

This note concerns the paper by Benslimane et Gadhi (JMAA. doi: 10.1016/j.jmaa.2023.127117) where the authors established necessary optimality conditions for an optimization problem (P) governed by a double phase partial di§erential equation (Pf): Having noticed inconsistencies between the investigated problem (Pf ) and the weak formulation of the equation that is associated with it, we propose some modiÖ- cations that, from our perspective, correct the forthmentioned issue. Some careless mistakes and typos that caught our interest are also underlined and rectiÖed.

math.AP↗
arXiv2022

Existence of solutions for a singular double phase in Sobolev-Orlicz spaces with variable exponents in a complete manifold

The purpose of this paper is to study a class of double phase problems, with a singular term and a superlinear parametric term on the right-hand side. Using the method of Nehari manifold combined with the fibering maps, we prove that for all small values of the parameter λ > 0, there exist at least two non-trivial positive solutions. Our results extend the previous works Papageorgiou, Repovus, and Vetro [24] and Liu, Dai, Papageorgiou, and Winkert [21], from the case of Musielak-Orlicz Sobolev space, when exponents p and q are constant, to the case of Sobolev-Orlicz spaces with variable exponents in a complete manifold.

math.AP↗
arXiv2021

Existence Results for double phase problem in Sobolev-Orlicz spaces with variable exponents in Complete Manifold

In this paper, we study the existence of non-negative non-trivial solutions for a class of double-phase problems where the source term is a Caratheodory function that satisfies the Ambrosetti-Rabinowitz type condition in the framework of Sobolev-Orlicz spaces with variable exponents in complete compact Riemannian n-manifolds. Our approach is based on the Nehari manifold and some variational techniques. Furthermore, the Hölder inequality, continuous and compact embedding results are proved.

math.AP↗
arXiv2021

Nonlinear Elliptic Equations With Variable Exponents Satisfying Cerami Condition

We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems involving the (p(x), q(x))-equation and the nonlinearity is superlinear but does not satisfy the usual Ambrossetti-Rabinowitz condition in the framework of Sobolev spaces with variable exponents in Complete manifolds. The main results are established by means of the mountain pass theorem and Fountain theorem with Cerami condition. Moreover, we are giving an example of a (p(x), q(x)) equation that verifies all our demonstrated results.

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