192 citations · 305 across the 24 of their papers we have counts for
25 papers
A new class of nonlocal operators: the fractional logarithmic -Laplacian and its properties
Anouar Bahrouni, Abdelhamid Gouasmia, Hichem Hajaiej +1
In this paper, we introduce and investigate the fractional logarithmic -Laplacian , defined as the first-order derivative with respect to the parameter of…
A Unified Truncation Method for Infinitely Many Solutions Without Symmetry
Anouar Bahrouni
This paper establishes the existence of infinitely many solutions for nonlinear problems without any symmetry, achieving three major advances. First, in the setting of semilinear e…
The concentration-compactness principle for Musielak-Orlicz spaces and applications
Ala Eddine Bahrouni, Anouar Bahrouni
This paper extends the Concentration-Compactness Principle to Musielak-Orlicz spaces, working in both bounded and unbounded domains. We show that our results include important spec…
A Class of De Giorgi Type and Hölder Continuity for Some Problems in Musielak-Orlicz-Sobolev Spaces
Hlel Missaoui, Anouar Bahrouni, Hichem Ounaies
In this paper, we introduce a new class of De Giorgi type functions, denoted by \(\mathcal{B}_{G(x,t)}\), and establish the Hölder continuity of its elements under suitable additio…
Global Existence and Finite-Time Blow-Up of Solutions for Parabolic Equations Involving the Fractional Musielak -Laplacian
Rakesh Arora, Anouar Bahrouni, Nitin Kumar Maurya
In this work, we study the parabolic fractional Musielak -Laplacian equation: \begin{equation*} \left\{ \begin{aligned} u_{t} + (-Δ)_{{g}_{x,y}}^{s} u &= f(x,u), && \text{…
Double phase problems with variable exponents depending on the solution and the gradient in the whole space
Ala Eddine Bahrouni, Anouar Bahrouni, Patrick Winkert
In this paper, we establish continuous and compact embeddings for a new class of Musielak-Orlicz Sobolev spaces in unbounded domains driven by a double phase operator with variable…
A new class of anisotropic double phase problems: exponents depending on solutions and their gradients
Ala Eddine Bahrouni, Anouar Bahrouni, Hlel Missaoui
In this work, we introduce two novel classes of quasilinear elliptic equations, each driven by the double phase operator with variable exponents. The first class features a new dou…
Maximum principles and moving planes method for the fractional -Laplacian
Anouar Bahrouni, Abdelhakim Sahbani, Ariel Salort
In this paper, we investigate the monotonicity of solutions for a nonlinear equations involving the fractional Laplacian with variable exponent. We first prove different maximum pr…
Existence and Multiplicity of Normalized Solutions for Dirac Equations with non-autonomous nonlinearities
Anouar Bahrouni, Qi Guo, Hichem Hajaiej +1
In this paper, we study the following nonlinear Dirac equations \begin{align*} \begin{cases} -i\sum\limits_{k=1}^3α_k\partial_k u+mβu=f(x,|u|)u+ωu, \displaystyle \int_{\mathbb{R}^3…
On the fractional Musielak-Sobolev spaces in R^d: Embedding results & applications
Anouar Bahrouni, Hlel Missaoui, Hichem Ounaies
This paper deals with new continuous and compact embedding theorems for the fractional Musielak-Sobolev spaces in . As an application, using the variational methods,…
On the Schrödinger-Bopp-Podolsky system: Ground state & least energy nodal solutions with nonsmooth nonlinearity
Anouar Bahrouni, Hlel Missaoui
In this work, we study the existence of sign-changing solutions for the Schrödinger-Bopp-Podolsky system.
Normalized Solutions to the mixed fractional Schrodinger equations with potential and general nonlinear term
Anouar Bahrouni, Qi Guo, Hichem Hajaiej
The purpose of this paper is to establish the existence of solutions with prescribed norm to a class of nonlinear equations involving the mixed fractional Laplacians. This type of…
Fractional double phase Robin problem involving variable order-exponents and Logarithm-type nonlinearity
Reshmi Biswas, Anouar Bahrouni, Alessio Fiscella
In this paper, we study the existence of solutions for the new fractinal Robin equations with variable exponents. Moreover, we deal with the logarithm-type nonlinearity. In particu…
Orlicz-Sobolev versus Hölder local minimizer for nonlinear Robin problems
Anouar Bahrouni, Hlel Missaoui, Hichem Ounaies +1
In this paper, we establish a regularity results for weak solutions of Robin problems driven by the well-known Orlicz -Laplacian operator. Precisely, by using a suitable variati…
Nonvariational and singular double phase problems for the Baouendi-Grushin operator
Anouar Bahrouni, Vicenţiu D. Rădulescu, Dušan D. Repovš
In this paper we introduce a new double phase Baouendi-Grushin type operator with variable coefficients. We give basic properties of the corresponding functions space and prove a c…
Least-energy nodal solutions of nonlinear equations with fractional Orlicz-Sobolev spaces
Anouar Bahrouni, Hlel Missaoui, Hichem Ounaies
In our work, we prove the existence of least-energy nodal solutions for nonlinear equations in which the new fractional Orlicz Laplacian is present. Precisely, we prove a compact e…
Algebraic topological techniques for elliptic problems involving fractional Laplacian
A. Panda, D. Choudhuri, A. Bahrouni
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to…
Low perturbations for a class of nonuniformly elliptic problems
Anouar Bahrouni, Dušan D. Repovš
We introduce and study a new functional which was motivated by our paper on the Caffarelli-Kohn-Nirenberg inequality with variable exponent (Bahrouni, Rădulescu and Repovš, Nonline…
Robin fractional problems with symmetric variable growth
Anouar Bahrouni, Vicentiu Radulescu, Patrick Winkert
In this paper we study the fractional p(., .)-Laplacian and we introduce the corresponding nonlocal conormal derivative for this operator. We prove basic properties of the correspo…
Remarks on Eigenvalue Problems for Fractional -Laplacian
Anouar Bahrouni, Ky Ho
In this paper, we give some properties and remarks of the new fractional Sobolev spaces with variable exponents. We also study the eigenvalue problem involving the new fractional $…
Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves
Anouar Bahrouni, Vicenţiu D. Rădulescu, Dušan D. Repovš
In this paper we are concerned with a class of double phase energy functionals arising in the theory of transonic flows. Their main feature is that the associated Euler equation is…
A Brezis-Lieb-type Lemma in Orlicz space
Anouar Bahrouni
In this work, we extend the well known Brezis-Lieb Lemma to the Orlicz space.
A note on the existence results for Schrodinger-Maxwell system with super-criticalnonlinearitie
Anouar Bahrouni
The paper considers the Schrodinger-Maxwell system with supercritical nonlinearitie. We prove the existence of at least one non-trivial weak solution. This result is already known…
A weighted anisotropic variant of the Caffarelli-Kohn-Nirenberg inequality and applications
Anouar Bahrouni, Vicenţiu D. Rădulescu, Dušan D. Repovš
We present a weighted version of the Caffarelli-Kohn-Nirenberg inequality in the framework of variable exponents. The combination of this inequality with a variant of the fountain…