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

摘要

We consider sign-changing solutions of the equation where and 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.