Some nonexistence results for positive solutions of elliptic equations in unbounded domains. (Q1880517)

Summary: 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.