A result on Hardy-Sobolev critical elliptic equations with boundary singularities

Jinhui Chen; Haitao Yang

doi:10.3934/cpaa.2007.6.191

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2007, Volume 6, Issue 1: 191-201. Doi: 10.3934/cpaa.2007.6.191

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A result on Hardy-Sobolev critical elliptic equations with boundary singularities

Jinhui Chen^1, and
Haitao Yang^1,

1.
Department of Mathematics, Zhejiang University, Hangzhou 310027

Received: December 31, 2005

Revised: August 31, 2006

Published: February 2007

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Abstract

In this note, a Hardy-Sobolev critical elliptic equation with boundary singularities and sublinear perturbation is studied. We obtain a result on the existence of classical solution and the multiplicity of weak solutions by making use of sub-super solutions and variational methods.

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Mathematics Subject Classification: Primary: 35j05, 35j25; Secondary: 35B40.

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