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Infinitely many arbitrarily small solutions for singular elliptic problems with critical Sobolev–Hardy exponents

Published online by Cambridge University Press:  02 February 2009

Xiaoming He
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China (wzou@math.tsinghua.edu.cn) Department of Mathematical Sciences, Central University of Nationalities, Beijing 100081, People's Republic of China (xmhe923@126.com)
Wenming Zou
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China (wzou@math.tsinghua.edu.cn)
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Abstract

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Let Ω ⊂ ℝN be a bounded domain such that 0 ∈ Ω, N ≥ 3, 2*(s) = 2(Ns)/(N − 2), 0 ≤ s < 2, . We obtain the existence of infinitely many solutions for the singular critical problem with Dirichlet boundary condition for suitable positive number λ.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2009