Elliptic equations with decaying cylindrical potentials and power-type nonlinearities
type: Item
instance of: scholarly article
title: Elliptic equations with decaying cylindrical potentials and power-type nonlinearities
zbMATH Open document ID: 1158.35032
author: M. Badiale
author: Michela Guida
author: Sergio Rolando
published in: Advances in Differential Equations
publication date: 2008-09-12T00:00:00Z
review text: The authors study the following cylindrical nonlinear elliptic equation: \[ -\Delta u+\frac{A}{| y| ^\alpha}u=f(u), \] where \(x=(y,z)\in \mathbb{R}^k\times\mathbb{R}^{N-k}\) (\(2\leq k<N\)), \(A, \alpha >0\), and \(f\) is a nonlinearity of power growth \(p\). Main results concern existence, nonexistence and asymptotic behavior of solutions, and rely on certain compatibility conditions between the exponents \(\alpha\) and \(p\). The proof of existence uses critical point theory.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 5343713
zbMATH Keywords: nonlinear elliptic equations
zbMATH Keywords: variational methods
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5343713