Some remarks on a system of quasilinear elliptic equations (Q1849343)

The present paper deals with the functional \[ \Phi(u,v)= {1\over p} \int_\Omega |\nabla u|^p+ {1\over q}\int_\Omega|\nabla v|^q-\int_\Omega F(x,u,v)\,dx, \tag{1} \] where \(p\) and \(q\) are real numbers larger than \(1,\Omega\) is some bounded domain in \(\mathbb R^N\), \(u\) and \(v\) are real-valued functions defined in \(\overline\Omega\) and belonging to appropriate spaces of functions and \(F\) is a potential. The goal of the authors is to study the geometry of this functional viewing to determining its critical points.