## Revista Matemática Iberoamericana

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 2 April 2004

http://projecteuclid.org/euclid.rmi/1080928420

Mathematical Reviews number (MathSciNet)
MR2076772

Zentralblatt MATH identifier
02104138

#### Citation

Damascelli, Lucio; Gladiali, Francesca. Some nonexistence results for positive solutions of elliptic equations in unbounded domains. Rev. Mat. Iberoamericana 20 (2004), no. 1, 67--86. http://projecteuclid.org/euclid.rmi/1080928420.

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