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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
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