M. MOKHTARI Abdelhak

MCA

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Department

Mathematics Department

Research Interests

Analyse fonctionnelle des EDPs Analyse mathématiques et topologie Méthodes variationnelles et théorie de points critiques Opérateurs fractionnaires et problèmes singuliers

Contact Info

University of M'Sila, Algeria

Email : abdelhak.mokhtari@univ-msila.dz

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Recent Publications

2023-10-25

حياة و الأعمال الرياضية لابن قنفذ القسنطيني

حياة و الأعمال الرياضية لابن قنفذ القسنطيني
Citation

M. MOKHTARI Abdelhak, (2023-10-25), "حياة و الأعمال الرياضية لابن قنفذ القسنطيني", [national] Mathematics, Mathematics and society , University of M'sila

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2023-05-21

Existence, uniqueness and multiplicity of solutions for a class of fractional p-Kirchhof

This study investigates the existence and uniqueness of solutions for a class of Kirchhoff problems involving the fractional p-Laplacian operator and a singular nonlinearities. We also study the existence and infinitely many solutions but without the singular term and with a presence of a nonlinear term satisfies a growth assumption. Our proofs are based on variational methods and genus theory.
Citation

M. MOKHTARI Abdelhak, (2023-05-21), "Existence, uniqueness and multiplicity of solutions for a class of fractional p-Kirchhof", [national] Advanced Studies in Contemporary Mathematics , JANGJEON Mathematical Society

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2023-05-02

On the existence of fixed points for a class of operators on Hilbert spaces and applications

On the existence of fixed points for a class of operators on Hilbert spaces and applications
Citation

M. MOKHTARI Abdelhak, (2023-05-02), "On the existence of fixed points for a class of operators on Hilbert spaces and applications", [international] The first international conference on mathematical sciences and applications , 8 May 1945 Guelma university

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2022

Critical p(x)-Kirchhoff Problems Involving Variable Singular Exponent

In this paper, we investigate a class of critical p(x)-Kirchhoff problems with a singular term. A nontrivial positive solution is obtained by combining variational methods with an appropriate truncation argument.
Citation

M. MOKHTARI Abdelhak, (2022), "Critical p(x)-Kirchhoff Problems Involving Variable Singular Exponent", [national] Bulletin of the Iranian Mathematical Society , Iranian Mathematical Society

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A fractional p(x,⋅) -Laplacian problem involving a singular term

This paper deals with a class of singular problems involving the fractional p(x,.)-Laplace operator. Using the direct method of minimization combined with the
theory of fractional Sobolev spaces with variable exponents, we prove that the problem has one positive solution for k[0 small enough. To our best knowledge, this paper is one of the first attempts in the study of singular problems involving fractional p(x,.)-Laplace operators.
Citation

M. MOKHTARI Abdelhak, (2022), "A fractional p(x,⋅) -Laplacian problem involving a singular term", [national] Indian Journal of Pure and Applied Mathematics , The Indian National Science Academy

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Mountain pass solutions and multiplicity result for a fractional p(x, ·)-Kirchhoff type problem

The purpose of this paper is to study the existence and infinitely many solutions for a some type of nonlocal p(\cdot,\cdot)-Kirchhoff problems with Dirichlet boundary conditions. Our proofs are based on variational methods, the Mountain Pass Lemma, and genus theory.
Citation

M. MOKHTARI Abdelhak, (2022), "Mountain pass solutions and multiplicity result for a fractional p(x, ·)-Kirchhoff type problem", [national] The First National Conference on Nonlinear Analysis, Theory and Applications (NATA’22) , University of Chlef

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Variational methods for some nonlinear problems

Variational methods are a valuable tool in the analysis of nonlinear problems. According to these methods, we are
trying to find solutions of a given nonlinear equation, by looking for critical points of a functional defined on the
function space in which we want the solution of our problem
Citation

M. MOKHTARI Abdelhak, (2022), "Variational methods for some nonlinear problems", [national] 6th M’sila Conference on Mathematical Analysis , University of M'sila

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2021-05-19

Espaces vectoriels normés

Je présente ce polycopie à mes chers étudiants dans lequelle j’ai rassemblé des leçons, des exercices résolus et autre proposés et quelques sujets d’examens qui constituent un résultat de mes conférences et travaux dirigés aux étudiants de troisième année licence dans le cadre du module "Espaces vectoriels normés" et ceci au niveau de département de mathématiques, université de M’sila.
Citation

M. MOKHTARI Abdelhak, (2021-05-19), "Espaces vectoriels normés", [national] University of M'sila

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2021

A fractional p(x, .)-Laplacian problem involving a singular term

Using the direct method of minimization combined with the theory of fractional Sobolev spaces with variable exponents, we prove that the problem has one positive solution for $\lambda>0$ small enough. To our best knowledge, this paper is one of the first attempts in the study of singular problems involving fractional $p(x,\cdot)$-Laplace operators.
Citation

M. MOKHTARI Abdelhak, (2021), "A fractional p(x, .)-Laplacian problem involving a singular term", [national] The second national mathematics seminar 2021, , l’université frères Mentouri Constantine 1

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2019

Existence and uniqueness of solutions for a p(x)-Laplacian problem in R^N.

we establish the existence and uniqueness of solutions for a $p(x)$-Laplacian equation in $\mathbb{R}^N$. The proof is based on variable exponent Sobolev space theory and the
Browder-Minty theorem.
Citation

M. MOKHTARI Abdelhak, (2019), "Existence and uniqueness of solutions for a p(x)-Laplacian problem in R^N.", [international] 3-ème colloque international sur la théorie des opérateurs, EDP et ses applications (CITO’ 2019) , Université d’Eloued, Algérie

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2016-06-22

Sur l’existence de solutions pour une classe de problèmes aux limites via la théorie des points critiques

Le travail dans cette thèse porte sur l’étude des solutions de quelques problèmes aux limites.
Citation

M. MOKHTARI Abdelhak, (2016-06-22), "Sur l’existence de solutions pour une classe de problèmes aux limites via la théorie des points critiques", [national] Ecole Normale Supérieure - Kouba, Alger

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2016

MULTIPLICITY RESULTS FOR AN IMPULSIVE BOUNDARY VALUE PROBLEM OF p(t)-KIRCHHOFF TYPE VIA CRITICAL POINT THEORY

In this paper we obtain existence results of k distinct pairs nontrivial solutions for an impulsive boundary value problem of p(t)-Kirchhoff type under certain conditions on the
parameter λ.
Citation

M. MOKHTARI Abdelhak, (2016), "MULTIPLICITY RESULTS FOR AN IMPULSIVE BOUNDARY VALUE PROBLEM OF p(t)-KIRCHHOFF TYPE VIA CRITICAL POINT THEORY", [national] Opuscula Mathematica , AGH University Press

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2015

EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A p(x)-KIRCHHOFF TYPE PROBLEM VIA VARIATIONAL TECHNIQUES

This paper discusses the existence and multiplicity of solutions for a class of p(x)-Kirchhoff type problems with Dirichlet boundary data
Citation

M. MOKHTARI Abdelhak, (2015), "EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A p(x)-KIRCHHOFF TYPE PROBLEM VIA VARIATIONAL TECHNIQUES", [national] ARCHIVUM MATHEMATICUM (BRNO) , Department of Mathematics, Faculty of Science of Masaryk University, Brno

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