A Liouville-type theorem for the \(p\)-Laplacian with potential term (Q2480284)

In the present study the authors use positivity properties to prove a general comparison principle for equations of the form \[ -\Delta_p u+ V|u|^{p-2} u= 0\quad\text{in }\Omega, \] where \(p\in (1,\infty)\), \(\Delta_p(u):= \nabla\cdot(|\nabla u|^{p-2}\nabla u)\) and \(V\in L^\infty_{\text{loc}}(\Omega;\mathbb{R})\).