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

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.