Some nonexistence results for positive solutions of elliptic equations in unbounded domains

Abstract

We prove some Liouville type theorems for positive solutions of semilinear elliptic equations in the whole space \mathbb{R}^N , N\geq 3 , and in the half space \mathbb{R}^N_{+} with different boundary conditions, using the technique based on the Kelvin transform and the Alexandrov-Serrin method of moving hyperplanes. In particular we get new nonexistence results for elliptic problems in half spaces satisfying mixed (Dirichlet-Neumann) boundary conditions.