# Vol 13 - Numéro 4 (Septembre 2022)

## Articles parus

Existence et multiplicité de solutions d’un problème elliptique non-local à exposant variable avec conditions aux limites non-lineaires

Using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian elliptic systems with Nonlinear boundary conditions.

Une nouvelle géneralisation des nombres de Genocchi et conséquence sur les polynômes de Bernoulli

This paper presents a new generalization of the Genocchi numbers and the Genocchi theorem. As consequences, we obtain some important families of integer-valued polynomials those are closely related to the Bernoulli polynomials. Denoting by ${(B_n)}_{n \in \mathbb{N}}$ the sequence of the Bernoulli numbers and by ${(B_n(X))}_{n \in \mathbb{N}}$ the sequence of the Bernoulli polynomials, we especially obtain that for any natural number $n$, the reciprocal polynomial of the polynomial $\big(B_n(X) - B_n\big)$ is integer-valued.

Transformation de Shearlet modulée continue

We generalize the well-known transforms such as short-time Fourier transform, wavelet transform and shearlet transform and refer it as Continuous Modulated Shearlet Transform. Important properties like Plancherel formula and inversion formula have been investigated. Uncertainty inequalities associated with this transform are presented.

Approches de points critiques pour les problèmes discrets anisotropes de type Kirchhoff

In this paper, we study a discrete anisotropic Kirchho type problem using variational methods and critical point theory, and we discuss the existence of two solutions for the problem. A example is presented to demonstrate the application of our main results.