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

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Abstract

We prove some Liouville type theorems for positive solutions of semilinear elliptic equations in the whole space ℝN, N ≥ 3, and in the half space 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.

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Damascelli, L., & Gladiali, P. (2004). Some nonexistence results for positive solutions of elliptic equations in unbounded domains. Revista Matematica Iberoamericana, 20(1), 67–86. https://doi.org/10.4171/rmi/380

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