Advances in Differential Equations

Elliptic equations with decaying cylindrical potentials and power-type nonlinearities

Marino Badiale, Michela Guida, and Sergio Rolando

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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

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

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 47J30: Variational methods [See also 58Exx]


Badiale, Marino; Guida, Michela; Rolando, Sergio. Elliptic equations with decaying cylindrical potentials and power-type nonlinearities. Adv. Differential Equations 12 (2007), no. 12, 1321--1362.

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