Geodesic
On the Absence of Positive Solutions of Elliptic Equations in Plane Unbounded Domains
Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 261-272.

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Using model equations of the form $\Delta u+u^\sigma=0$ as an example, in both linear ($\sigma=1$) and nonlinear ($\sigma>1$) cases, we show some direct methods of proof of the absence of positive solutions in semi-infinite plane domains. We consider semi-infinite strips, both straight and exponentially decreasing, with homogeneous Neumann condition on the upper and lower boundaries.
Mots-clés : elliptic equation, Neumann condition.
Keywords: model equation, semi-infinite strip 
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S. I. Pokhozhaev. On the Absence of Positive Solutions of Elliptic Equations in Plane Unbounded Domains. Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 261-272. http://geodesic.mathdoc.fr/item/MZM_2009_85_2_a8/

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