On the singular elliptic problem involving the variable order fractional Musielak g_x,y-Laplacian

2025/12/08 by Baalal, Azeddine, Berghout, Mohamed, Ouali, El-Houcine
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2512.07645

Abstract

In this paper, we investigate the existence of positive weak solutions to a nonlocal singular elliptic problem under Dirichlet boundary condition. Problem is settled in fractional Musielak-Sobolev spaces with variable order. The main tool is variational approach, however, various auxiliary tools from the theory of nonlinear functional analysis, convex analysis and critical point theory are also applied.

Citations

• Eigenvalue type problem in s(.,.)-fractional Musielak-Sobolev spaces
• Embedding and extension results in Fractional Musielak-Sobolev spaces
• Embedding theorems in the fractional Orlicz-Sobolev space and\n applications to non-local problems
• Variable order nonlocal Choquard problem with variable exponents
• Basic results of fractional Orlicz-Sobolev space and applications to non-local problems
• Some approximation results in Musielak-Orlicz spaces
• Fractional order Orlicz-Sobolev spaces

Related

• Existence and uniqueness of solutions in fractional Orlicz-Sobolev spaces for a nonlocal singular elliptic problem
• On the singular problem involving g-Laplacian
• Existence and multiplicity of solutions for a Dirichlet problem in Fractional Orlicz- Sobolev spaces
• Extremals For Fractional Order Hardy-Sobolev-Maz'ya Inequality
• Existence, Uniqueness of Positive Solution to a Fractional Laplacians with Singular Nonlinearity