Volume 32, Issue 2

In this paper, we consider a hyperbolic perturbation of the 2D Navier–Stokes equations, which consists in adding the term ε ⁢ u t ⁢ t {\varepsilon u_{tt}} to the Navier–Stokes equations. We prove the global persistence of analyticity and Gevrey-class of solutions. Moreover, we prove that the solution to the perturbed Navier–Stokes equations approximates the solution to the classical Navier–Stokes equations.

In this paper, we prove some new discrete inequalities with weights of Hardy’s type and employ them to establish some properties of discrete weighted Gehring class of sequences satisfying reverse Hölder inequality. We also consider the weighted class of sequences satisfying a reverse inequality for nonincreasing sequences and prove some higher summability theorems.

The aim of this paper is to introduce the new class of left and right B-Weyl operators, which naturally extends the conventional concepts of left and right Weyl operators. Our contributions encompass demonstrating the stability of the left (and right) B-Weyl operators under small perturbations. We further characterize the left (and right) B-Weyl operators as the direct sum of a closed left (and right) Drazin invertible operator and a finite rank operator. Additionally, we present some characterizations of the left and right B-Weyl spectra, utilizing the left and right Drazin spectra as essential components. Furthermore, our obtained results play a pivotal role in exploring the interrelations between the left and right B-Weyl spectra and other spectra integral to the realm of B-Fredholm theory. This paper seeks to enhance and extend the recent research explored in [F. Abdmouleh and T. Ben Lakhal, Left and right B-Fredholm operators, Ukrainian Math. J. 74 2023, 10, 1479–1489] to a larger class in the unbounded B-Fredholm operators theory.

The aim of this work is the study of a nonlinear boundary value problem which theoretically generalizes the Lamé system with disturbance in a thin 3D domain with friction and a generalized boundary condition. For the resolution of the considered problem and after the variational formulation, we construct an operator from the variational problem. Then we prove that this operator has certain properties which allows us to apply the theorem of existence and uniqueness of the solution of variational inequalities of the 2nd kind. Finally, using a change of scale, we transport the variational problem to an equivalent problem defined on a domain independent of the parameter ζ {{\zeta}} and subsequently we obtain the limit problem and the generalized weak equations of the initial problem.

In the present paper we investigate three-dimensional dynamical mixed boundary-transmission problems for composed body consisting of two adjacent anisotropic elastic components having a common interface surface. The two contacting elastic components are subject to different mathematical models: Green–Lindsay’s model of generalized thermo-electro-magneto-elasticity in one component and Green–Lindsay’s model of generalized thermo-elasticity in the other one. We assume that the composed elastic structure under consideration contains an interfacial crack. We prove the uniqueness and existence theorems in appropriate function spaces.

In this note we prove weighted Rellich–Sobolev and Hardy–Sobolev inequalities in variable exponent Lebesgue spaces L p ⁢ ( ⋅ ) ⁢ ( 𝔾 ) {L^{p(\,\cdot\,)}(\mathbb{G})} defined on stratified homogeneous groups 𝔾 {\mathbb{G}} . To derive the main results, we rely on weighted estimates for the Riesz potential operators in L p ⁢ ( ⋅ ) ⁢ ( 𝔾 ) {L^{p(\,\cdot\,)}(\mathbb{G})} , where 𝔾 {{\mathbb{G}}} is a general homogeneous group. The results are new even for the Abelian (Euclidean) case 𝔾 = ( ℝ d , + ) {\mathbb{G}=(\mathbb{R}^{d},+)} and the Heisenberg groups 𝔾 = ℍ n {\mathbb{G}={\mathbb{H}}^{n}} . The main statements are obtained for variable exponents satisfying the condition that the Hardy–Littlewood maximal operator is bounded in appropriate variable exponent Lebesgue spaces. We also give some quantitative estimates for the norms of integral operators involved in derived estimates.

In this paper, we consider a class of p ⁢ ( x ) {p(x)} -Laplacian like problems with indefinite weight involving no flux boundary condition. Using variational techniques and the critical point theorem of Bonanno and Marano [4], we prove the existence of at least three weak solutions to the problem in Sobolev variable exponent spaces.

In this work, a time-antiperiodic and space-periodic boundary value problem for one class of semilinear partial differential equations is studied. The theorems on existence, uniqueness and nonexistence of solutions of this problem are proved.

The aim of this paper is to transfer the restrictedness theory to Hom-Lie algebras. The concept of restricted Hom-Lie algebras, which is introduced in [S. Bouarroudj and A. Makhlouf, Hom-lie superalgebras in characteristic 2, Mathematics 11 2023, 24, Paper No. 4955], will be used in this paper. First, the existence and uniqueness of p -structures on a Hom-Lie algebra is studied. Then the definition of a restrictable Hom-Lie algebra is given and the equivalence relation between restrictable Hom-Lie algebras and restricted Hom-Lie algebras is constructed. Finally, the p -envelopes of a Hom-Lie algebra are defined and studied.

In this paper, we use the variational method to study some singular Steklov-type problem with variable exponents. More precisely, we use the min-max method in order to prove the existence of a solution to such a problem.

In the present work, we explore Fejér-type operators within the mixed Lebesgue space L p → ⁢ [ ℝ 2 ] {L_{\vec{p}}[\mathbb{R}^{2}]} and establish the degree of approximation for functions belonging to the class H p → η 1 , η 2 {H_{\vec{p}}^{\eta_{1},\eta_{2}}} through the utilization of Fejér-type operators.

This paper aims to determine the maximum number of limit cycles that can bifurcate from the linear center x ˙ = y {\dot{x}=y} , y ˙ = - x {\dot{y}=-x} , when we perturb it inside a class of piecewise smooth differential systems, which are separated by the straight line y = 0 {y=0} . Using the averaging theory of first order for piecewise smooth differential systems, we prove that if the degree of the polynomial that appears in the perturbation term is equal to n , then the maximum number of limit cycles bifurcating from the period annulus around the linear center is at most n or n - 1 {n-1} , and this number can be reached.

Marcinkiewicz spaces with variable exponents are defined and some basic properties are given.

In this note, we study the generalized fraction properties and power series properties of 𝒮 {\mathcal{S}} -Noetherian rings. Actually, we investigate two questions proposed in [A. Dabbabi and A. Benhissi, Generalization of the S -Noetherian concept, Arch. Math. (Brno) 59 2023, 4, 307–314].

In this present paper, we are first of all interested in some continuity and compactness results for the space ψ-fractional 𝕊 𝒜 α , β ; ψ ⁢ ( Λ ) {\mathbb{S}^{\alpha,\beta;\psi}_{\mathcal{A}}(\Lambda)} . In this sense, we investigate the existence of at least two solutions with constant signs using truncation arguments and comparison methods of a new class of fractional differential equations with m ⁢ ( ξ ) {m(\xi)} -Laplacian with double phase.