<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we study a class of fractional <italic>p</italic>(<italic>x</italic>)-Laplacian Dirichlet problems in a bounded domain with Lipschitz boundary. Using variational methods, we prove in different situations the existence and multiplicity of solutions.
</abstract>

University Moulay Ismail of Meknes, FST Errachidia

Existence and multiplicity results for fractional <italic>p</italic>(<italic>x</italic>)-Laplacian Dirichlet problem

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper we prove the existence of at least one renormalized solution for the p(x)-Laplacian equation associated with a maximal monotone operator and Radon measure data. The functional setting involves Sobolev spaces with variable exponent <italic>W</italic>1,<italic>p</italic>(·)(Ω).
</abstract>

Renormalized solutions for a <italic>p</italic>(·)-Laplacian equation with Neumann nonhomogeneous boundary condition involving diffuse measure data and variable exponent

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we study the following nonlinear eigenvalue problem:
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0013_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mo>{</mo> <mrow><mtable><mtr><mtd><mrow><msup><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><mn>2</mn><mi>p</mi></mrow></msup><mi>u</mi><mo>=</mo><mi>λ</mi><mi>m</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mi> </mi><mi> </mi><mi> </mi><mi>i</mi><mi>n</mi><mi> </mi><mi> </mi><mi mathvariant="normal">Ω</mi><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>u</mi><mo>=</mo><mi mathvariant="normal">Δ</mi><mi>u</mi><mo>=</mo><mo>…</mo><msup><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><mn>2</mn><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mo>=</mo><mn>0</mn><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mi>o</mi><mi>n</mi><mi> </mi><mi> </mi><mo>∂</mo><mi mathvariant="normal">Ω</mi><mo>.</mo></mrow></mtd></mtr></mtable></mrow> </mrow></mrow></math>
<tex-math>\left\{ {\matrix{ {{\Delta ^{2p}}u = \lambda m\left( x \right)u\,\,\,in\,\,\Omega ,} \cr {u = \Delta u = \ldots {\Delta ^{2p - 1}}u = 0\,\,\,\,on\,\,\partial \Omega .} \cr } } \right.</tex-math>
</alternatives>
</disp-formula>
Where Ω is a bounded domain in ℝ<italic>N</italic> with smooth boundary ∂ Ω, <italic>N ≥</italic> 1, <italic>p</italic> ∈ ℕ*, <italic>m</italic> ∈ <italic>L∞</italic> (Ω), <italic>µ</italic>{<italic>x</italic> ∈ Ω: <italic>m</italic>(<italic>x</italic>) > 0} ≠ 0, and Δ2<italic>pu</italic> := Δ (Δ...(Δ<italic>u</italic>)), 2<italic>p</italic> times the operator Δ.
Using the Szulkin’s theorem, we establish the existence of at least one non decreasing sequence of nonnegative eigenvalues.
</abstract>

Mathematics and Computer Science Department

Existence of solutions for 4p-order PDES

<abstract xmlns="http://www.w3.org/1999/xhtml">

The aim of this paper is to give some new characterizations of strictly Lipschitz <italic>p</italic>-summing operators. These operators have been introduced in order to improve the Lipschitz <italic>p</italic>-summing operators. Therefore, we adapt this definition for constructing other classes of Lipschitz mappings which are called strictly Lipschitz <italic>p</italic>-nuclear and strictly Lipschitz (<italic>p</italic>, <italic>r</italic>, <italic>s</italic>)-summing operators. Some interesting properties and factorization results are obtained for these new classes.
</abstract>

Laboratoire d’Analyse Fonctionnelle et Géométrie des Espaces

Further results on strictly Lipschitz summing operators

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we investigate the existence of sign-changing solutions for the following class of fractional Kirchhoff type equations with potential
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0015_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mi>b</mi><msubsup><mrow><mrow><mrow><mo>[</mo> <mi>u</mi> <mo>]</mo></mrow></mrow></mrow><mi>α</mi><mn>2</mn></msubsup></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><msup><mrow><mrow><mrow><mo>(</mo><mrow><mo>-</mo><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mi>x</mi></msub></mrow><mo>)</mo></mrow></mrow></mrow><mi>α</mi></msup><mi>u</mi><mo>-</mo><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mi>y</mi></msub><mi>u</mi></mrow><mo>)</mo></mrow><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mo>)</mo></mrow><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi></mrow><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mi>ℝ</mi></mrow><mi>N</mi></msup><mo>=</mo><msup><mrow><mi>ℝ</mi></mrow><mi>n</mi></msup><mo>×</mo><msup><mrow><mi>ℝ</mi></mrow><mi>m</mi></msup><mo>,</mo></mrow></math>
<tex-math>\left( {1 + b\left[ u \right]_\alpha ^2} \right)\left( {{{\left( { - {\Delta _x}} \right)}^\alpha }u - {\Delta _y}u} \right) + V\left( {x,y} \right)u = f\left( {x,y,u} \right),\left( {x,y} \right) \in {\mathbb{R}^N} = {\mathbb{R}^n} \times {\mathbb{R}^m},</tex-math>
</alternatives>
</disp-formula>
where <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0015_eq_002.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mrow><mrow><mo>[</mo> <mi>u</mi> <mo>]</mo></mrow></mrow></mrow><mi>α</mi></msub><mo>=</mo><msup><mrow><mrow><mrow><mo>(</mo><mrow><mrow><mo>∫</mo><mrow><msub><mrow></mrow><mrow><msup><mrow><mi>ℝ</mi></mrow><mi>N</mi></msup></mrow></msub><mrow><mo>(</mo><mrow><msup><mrow><mrow><mrow><mo>|</mo> <mrow><msup><mrow><mrow><mrow><mo>(</mo><mrow><mo>-</mo><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mi>x</mi></msub></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mfrac><mi>α</mi><mn>2</mn></mfrac></mrow></msup><mi>u</mi></mrow> <mo>|</mo></mrow></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mrow><mo>|</mo> <mrow><msub><mrow><mo>∇</mo></mrow><mi>y</mi></msub><mi>u</mi></mrow> <mo>|</mo></mrow></mrow></mrow><mn>2</mn></msup></mrow><mo>)</mo></mrow><mi>d</mi><mi>x</mi><mi>d</mi><mi>y</mi></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></msup></mrow></math>
<tex-math>{\left[ u \right]_\alpha } = {\left( {\int {_{{\mathbb{R}^N}}\left( {{{\left| {{{\left( { - {\Delta _x}} \right)}^{{\alpha \over 2}}}u} \right|}^2} + {{\left| {{\nabla _y}u} \right|}^2}} \right)dxdy} } \right)^{{1 \over 2}}}</tex-math>
</alternatives>
</inline-formula>. Based on variational approach and a variant of the quantitative strain lemma, for each <italic>b ></italic> 0, we show the existence of a least energy nodal solution <italic>ub</italic>. In addition, a convergence property of <italic>ub</italic> as <italic>b</italic> ↘ 0 is established.
</abstract>

Oriental Applied Mathematics Laboratory(LAMO)

Least energy sign-changing solutions for a nonlocal anisotropic Kirchhoff type equation

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we are concerned with the study of the spectrum for the nonlinear Steklov problem of the form
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0016_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mo>{</mo> <mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mi>p</mi></msub><mi>u</mi><mo>=</mo><msup><mrow><mrow><mrow><mo>|</mo> <mi>u</mi> <mo>|</mo></mrow></mrow></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></msup><mi>u</mi></mrow></mtd><mtd columnalign="left"><mrow><mtext>in</mtext><mi> </mi><mi mathvariant="normal">Ω</mi><mo>,</mo></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow><msup><mrow><mrow><mrow><mo>|</mo> <mrow><mo>∇</mo><mi>u</mi></mrow> <mo>|</mo></mrow></mrow></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></msup><mfrac><mrow><mo>∂</mo><mi>u</mi></mrow><mrow><mo>∂</mo><mi>v</mi></mrow></mfrac><mo>=</mo><mi>λ</mi><msubsup><mrow><mrow><mrow><mo>‖</mo> <mi>u</mi> <mo>‖</mo></mrow></mrow></mrow><mrow><mi>q</mi><mo>,</mo><mo>∂</mo><mi mathvariant="normal">Ω</mi></mrow><mrow><mi>p</mi><mo>-</mo><mi>q</mi></mrow></msubsup><msup><mrow><mrow><mrow><mo>|</mo> <mi>u</mi> <mo>|</mo></mrow></mrow></mrow><mrow><mi>q</mi><mo>-</mo><mn>2</mn></mrow></msup><mi>u</mi></mrow></mtd><mtd columnalign="left"><mrow><mtext>on</mtext><mi> </mi><mo>∂</mo><mi mathvariant="normal">Ω</mi><mo>,</mo></mrow></mtd></mtr></mtable></mrow> </mrow></mrow></math>
<tex-math>\left\{ {\matrix{{{\Delta _p}u = {{\left| u \right|}^{p - 2}}u} \hfill &amp; {{\rm{in}}\,\Omega ,} \hfill \cr {{{\left| {\nabla u} \right|}^{p - 2}}{{\partial u} \over {\partial v}} = \lambda \left\| u \right\|_{q,\partial \Omega }^{p - q}{{\left| u \right|}^{q - 2}}u} \hfill &amp; {{\rm{on}}\,\partial \Omega ,} \hfill \cr } } \right.</tex-math>
</alternatives>
</disp-formula>
where Ω is a smooth bounded domain in ℝ<italic>N</italic>(<italic>N</italic> ≥ 1), λ is a real number which plays the role of eigenvalue and the unknowns <italic>u</italic> ∈ <italic>W</italic>1,<italic>p</italic>(Ω). Using the Ljusterneck-Shnirelmann theory on <italic>C</italic>1 manifold and Sobolev trace embedding we prove the existence of an increasing sequence positive of eigenvalues (λ<italic>k</italic>)<italic>k</italic>≥1, for the above problem. We then establish that the first eigenvalue is simple and isolated.
</abstract>

Department of Mathematics, Faculty of Sciences and Technologies Moulay Ismail University of Meknes

College of Science Al Imam Mohammad Ibn Saud Islamic University (IMSIU)

Faculty of Sciences Dhar El Mahraz University Sidi Mohamed Ben Abdellah

Steklov problems for the <italic>p</italic>−Laplace operator involving <italic>Lq</italic>-norm

<abstract xmlns="http://www.w3.org/1999/xhtml">

This paper is concerned with the Bayesian inference for the dependent parameters of stochastic SIR epidemic model in a closed population. The estimation framework involves the introduction of <italic>m</italic> − 1 latent data between every pair of observations. Kibble’s bivariate gamma distribution is considered as a good candidate prior density of parameters, they give an appropriate frame to model the dependence between the parameters. A Markov chain Monte Carlo methods are then used to sample the posterior distribution of the model parameters. Simulated datasets are used to illustrate the proposed methodology.
</abstract>

Applied Mathematics and Scientific Computing Laboratory

Department of Applied Mathematics, Faculty of Sciences and Techniques

C.P:523, Sultan Moulay Slimane University-Beni-Mellal

Bayesian Inference for SIR Epidemic Model with dependent parameters

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we are interested in some theoretical and numerical studies of a special case of a degenerate nonlinear Schrödinger equation namely the so-called Gross-Pitaevskii Equation(GPE). More precisely, we will treat in a first time the well-posedness of GPE model with a degeneracy occurring in the interior of the space variable domain, i.e ∃<italic>x</italic>0 ∈ (0, <italic>L</italic>), <italic>s</italic>. <italic>t k</italic>(<italic>x</italic>0) = 0, where <italic>k</italic> stands for the diffusion coefficient and <italic>L</italic> is a positive constant. Thereafter, we will focus ourselves on some numerical simulations showing the influence of a different parameters, especially the interior degeneracy, on the behavior of the wave solution corresponding to our model in a special case of the function <italic>k</italic> namely <italic>k</italic>(<italic>x</italic>) = |<italic>x</italic> − <italic>x</italic>0| α, <italic>α</italic> ∈ (0, 1).
</abstract>

Department of Mathematics, Faculty of Science and Technology

Laboratory of mathematics and population dynamics

Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation

<abstract xmlns="http://www.w3.org/1999/xhtml">

We study, from a quite general point of view, a CQ*-algebra (X, 𝖀0) possessing a sufficient family of bounded positive tracial sesquilinear forms. Non-commutative <italic>L</italic>2-spaces are shown to constitute examples of a class of CQ*-algebras and any abstract CQ*-algebra (X, 𝖀0) possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a direct sum of non-commutative <italic>L</italic>2-spaces.
</abstract>

CQ *-algebras of measurable operators

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Moroccan Journal of Pure and Applied Analysis

 The Moroccan Journal of Pure and Applied Analysis "MJPAA" (Print ISSN: 2605-6364) is a peer-reviewed open access journal published by the "Université Sidi Mohamed Ben Abdellah" (Sidi Mohamed Ben Abdallah University), covering all main-stream branches of pure and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, numerical analysis, optimization theory, and control theory.   MJPAA is published by Sidi Mohamed Ben Abdallah University in three issues in January, May and September.   Why subscribe and read    The journal covers a wide range of branches of mathematical analysis.   Pure and applied analysis topics are intensely studied by researchers throughout the world especially in Africa, the Arab and European countries.   An edition committee of high-level and international renown.   Editorial board representing different regions of the world and various research teams.      Why submit    No publication charges for the authors or their institutions.   The journal is available to be indexed in the most important databases.   The journal is among the best in its field in Africa and the Arab world.      Rejection Rate    45%      Archiving   Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.   Plagiarism Policy   The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.   Publisher:Sidi Mohamed Ben Abdallah University (Route Imouzzer, BP 2626 Fez 30000, Morocco, Tel. : 0212 5 35 60 96 60/ 61)   Contact:Professor Youssef Akdim, Sidi Mohamed Ben Abdellah Universitymjpaa.edition1@usmba.ac.ma 

Moroccan Journal of Pure and Applied Analysis

Volume 8 (2022): Issue 2 (May 2022)

Existence and multiplicity results for fractional p(x)-Laplacian Dirichlet problem

Renormalized solutions for a p(·)-Laplacian equation with Neumann nonhomogeneous boundary condition involving diffuse measure data and variable exponent

Existence of solutions for 4p-order PDES

Further results on strictly Lipschitz summing operators

Least energy sign-changing solutions for a nonlocal anisotropic Kirchhoff type equation

Steklov problems for the p−Laplace operator involving L^q-norm

Bayesian Inference for SIR Epidemic Model with dependent parameters

Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation

CQ *-algebras of measurable operators

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