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On inhomogeneous biharmonic equations involving critical exponents

Published online by Cambridge University Press:  14 November 2011

Yinbin Deng  and
Gengsheng Wang
Yinbin Deng
Affiliation:
Department of Mathematics Huazhong Normal University Wuhan 430079 People'sRepublic of China (ybdeng@public.wh.hb.cn)
Gengsheng Wang
Affiliation:
Department of Mathematics Huazhong Normal University Wuhan 430079 People'sRepublic of China (ybdeng@public.wh.hb.cn)
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Abstract

In this paper, we consider the existence of multiple solutions of biharmonic equations boundary value problem

where Ω is a bounded smooth domain in ℝN, N ≥ 5; λ ∈ ℝ1 is a given constant; p = 2N/(N − 4) is the critical Sobolev exponent for the embedding ; Δ2 = ΔΔ denotes iterated N-dimensional Laplacian; f(x) is a given function. Some results on the existence and non-existence of multiple solutions for the above problem have been obtained by Ekeland's variational principle and the mountain-pass lemma under some assumptions on f(x) and N.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 5 , 1999 , pp. 925 - 946
Copyright
Copyright © Royal Society of Edinburgh 1999

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