## Advances in Differential Equations

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

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

Marino Badiale, Michela Guida, and Sergio Rolando

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1355867405

**Mathematical Reviews number (MathSciNet)**

MR2382728

**Zentralblatt MATH identifier**

1158.35032

**Subjects**

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]

#### Citation

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. https://projecteuclid.org/euclid.ade/1355867405.