Weak Solutions for a System Involving Anisotropic \(\left( \overrightarrow{p}(\cdot ), \overrightarrow{q}(\cdot )\right) \)-Laplacian Operators

A system embracing the anisotropic \(\left( \overrightarrow{p}(\cdot ), \overrightarrow{q}(\cdot )\right) \) $\left(\overrightarrow{p},(·),,,\overrightarrow{q},(·)\right)$ -Laplacian operators is studied. We prove the existence and multiplicity of positive weak solutions for the system, via the critical point theory.