Liouville Results for m-Laplace Equations in Half-Space and Strips with Mixed Boundary Value Conditions and Finite Morse Index

Abstract

We consider sign-changing solutions of the equation \(-\Delta _m u= |u|^{p-1}u\) where \(m\ge 2\) and \(p>1\) in half-space and strips with nonlinear mixed boundary value conditions. We prove Liouville type theorems for stable solutions or for solutions which are stable outside a compact set. The main methods used are the integral estimates, the Pohozaev-type identity and the monotonicity formula.