### Elliptic equations with decaying cylindrical potentials and power-type nonlinearities

#### Abstract

We obtain existence, nonexistence and asymptotic results for solutions to cylindrical equations of the form: $-\triangle u+\frac{A}{\left| y\right| ^{\alpha }}u= f\left( u\right) ~\textrm{in }\mathbb{R}^{N},~ x=\left( y,z\right) \in \mathbb{R}^{k}\times \mathbb{R}^{N-k},~N>k\geq 2,$ where $A,\alpha>0$ and $f$ is continuous and satisfies power-type growth conditions.

#### Article information

Source
Adv. Differential Equations Volume 12, Number 12 (2007), 1321-1362.

Dates
First available in Project Euclid: 18 December 2012