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Nonlinear elliptic equations with critical potential and critical parameter

Published online by Cambridge University Press:  12 July 2007

Yao Tian Shen  and
Yang Xin Yao
Yao Tian Shen
Affiliation:
School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, People's Republic of [email protected]
Yang Xin Yao
Affiliation:
School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, People's Republic of [email protected]
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Abstract

We give a positive answer to an open problem about Hardy's inequality raised by Brézis and Vázquez, and another result obtained improves that of Vázquez and Zuazua. Furthermore, by this improved inequality and the critical-point theory, in a k-order Sobolev–Hardy space, we obtain the existence of multi-solution to a nonlinear elliptic equation with critical potential and critical parameter.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 5 , October 2006 , pp. 1041 - 1051
Copyright
Copyright © Royal Society of Edinburgh 2006

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