arXiv subjects

Nabil Chems Eddine

Publications and source records attributed to Nabil Chems Eddine.

4 recordsLinked to original sources

arXiv2024

Embeddings of anisotropic Sobolev spaces into spaces of anisotropic Hölder-continuous functions

We introduce a novel framework for embedding anisotropic variable exponent Sobolev spaces into spaces of anisotropic variable exponent Hölder-continuous functions within rectangular domains. We establish a foundational approach to extend the concept of Hölder continuity to anisotropic settings with variable exponents, providing deeper insight into the regularity of functions across different directions. Our results not only broaden the understanding of anisotropic function spaces but also open new avenues for applications in mathematical and applied sciences.

math.FA↗

arXiv2023

The Neumann problem for a class of generalized Kirchhoff-type potential systems

In this paper, we are concerned with the Neumann problem for a class of quasilinear stationary Kirchhoff-type potential systems, which involves general variable exponents elliptic operators with critical growth and real positive parameter. We show that the problem has at least one solution, which converges to zero in the norm of the space as the real positive parameter tends to infinity, via combining the truncation technique, variational method, and the concentration-compactness principle for variable exponent under suitable assumptions on the nonlinearities.

math.AP↗

arXiv2022

Multiple Solutions for Nonlinear Generalized-Kirchhoff type potential Systems in Unbounded Domains

In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems in unbounded domains, which involves a general variable exponent elliptic operator. Under some suitable conditions on the nonlinearities, we establish existence of at least three weak solutions for the problem. The proof of our main result uses variational methods and the critical theorem of Bonanno and Marano.

math.AP↗

arXiv2022

Generalized critical Kirchhoff-type potential systems With Neumann Boundary conditions

In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems with Neumann Boundary conditions, which involves a general variable exponent elliptic operator with critical growth. Under some suitable conditions on the nonlinearities, we establish existence and multiplicity of solutions for the problem by using the concentration-compactness principle of Lions for variable exponents found in [5, 7] and the Mountain Pass Theorem without the Palais-Smale condition given in [43].

math.AP↗