# zbMATH — the first resource for mathematics

Some nonexistence results for positive solutions of elliptic equations in unbounded domains. (English) Zbl 1330.35146
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.

##### MSC:
 35J60 Nonlinear elliptic equations 35B50 Maximum principles in context of PDEs
Full Text: