8 papers
On the fractional logarithmic -Laplacian
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 o…
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…
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 additi…
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…
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…
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…