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

Source: Rev. Mat. Iberoamericana Volume 20, Number 1 (2004), 67-86.

#### Abstract

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.

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Primary Subjects: 35B05, 35B45, 35B50
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.rmi/1080928420
Zentralblatt MATH identifier: 02104138
Mathematical Reviews number (MathSciNet): MR2076772

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