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Multiple solutions for nonhomogeneous elliptic equations involving critical Sobolev exponent*

Published online by Cambridge University Press:  14 November 2011

Dao-Min Cao ,
Gong-Bao Li  and
Huan-Song Zhou
Dao-Min Cao
Affiliation:
Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, P.R. China
Gong-Bao Li
Affiliation:
Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, P.R. China
Huan-Song Zhou
Affiliation:
Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, P.R. China
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Abstract

We consider the following problem:

where is continuous on RN and h(x)≢0. By using Ekeland's variational principle and the Mountain Pass Theorem without (PS) conditions, through a careful inspection of the energy balance for the approximated solutions, we show that the probelm (*) has at least two solutions for some λ* > 0 and λ ∈ (0, λ*). In particular, if p = 2, in a different way we prove that problem (*) with λ ≡ 1 and h(x) ≧ 0 has at least two positive solutions as

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 6 , 1994 , pp. 1177 - 1191
Copyright
Copyright © Royal Society of Edinburgh 1994

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