We prove some Liouville type theorems for positive solutions of semilinear elliptic equations in the whole space , , and in the half space 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.
Cite this article
Lucio Damascelli, Francesca Gladiali, Some nonexistence results for positive solutions of elliptic equations in unbounded domains. Rev. Mat. Iberoam. 20 (2004), no. 1, pp. 67–86