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2007 Elliptic equations with decaying cylindrical potentials and power-type nonlinearities
Marino Badiale, Michela Guida, Sergio Rolando
Adv. Differential Equations 12(12): 1321-1362 (2007).

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.

Citation

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Marino Badiale. Michela Guida. Sergio Rolando. "Elliptic equations with decaying cylindrical potentials and power-type nonlinearities." Adv. Differential Equations 12 (12) 1321 - 1362, 2007.

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1158.35032
MathSciNet: MR2382728

Subjects:
Primary: 35J60
Secondary: 35J20, 35Q55, 47J30

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.12 • No. 12 • 2007
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