Mokhtar Naceri

Existence Results for Nonlinear Weighted Anisotropic Elliptic Systems with Variable Exponents

abstract:
This paper establishes the existence of distributional solutions for a class of anisotropic elliptic $\vec{p}(\,\cdot\,)$-systems. These systems are weighted by a positive function that belongs to the $\vec{p}(\,\cdot\,)$-Sobolev space and involves $L^1(\Omega;\mathbb{R}^m)$-data associated with the $L^1(\Omega)$-coefficient of the zero order term.

Mathematics Subject Classification: 35J60, 35J66, 35J67

Key words and phrases: Nonlinear elliptic systems, weight function, $\vec{p}(\,\cdot\,)$-Sobolev spaces, variable exponents, distributional solution, existence