Infinitely many solutions to elliptic systems involving critical exponents and Hardy potential
Infinitely many solutions to elliptic systems involving critical exponents and Hardy potential
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DOI：
10.1002/mma.2669
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发表时间：
2013-06
影响因子：
2.9
通讯作者：
Li Wang
中科院分区：
文献类型：
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作者：
Li Wang
本文考虑具有临界Sobolev增长和哈代势的椭圆方程组：−Δu−λ1u| X| 2=a1| u| 2*−2u+bh（x）αα+β| u| α−2u| v| β，x∈RN，−Δv−λ2v| X| 2=a2| v| 2*−2v+bh（x）βα+β| u| α| v| β−2v，x∈RN，其中N ≥ 3，λ1，λ2 ∈ [0，ΛN），ΛN：=N−222是最佳的哈代常数。2*=2NN−2是临界Sobolev指数。a1，a2，B为正参数，α，β > 0且1 < α + β：= q < 2 < 2*。h（x）∈Lq′（RN），其中q′=2*2*−q。利用集中紧性原理和Kajikiya的对称山路引理的新版本，我们得到了无穷多个解，这些解对于适当的正参数a1，a2，B和λ1，λ2趋于零。版权所有© 2012约翰威利父子有限公司.
In this paper, we consider the following elliptic systems involving critical Sobolev growth and Hardy potential: −Δu−λ1u|x|2=a1|u|2*−2u+bh(x)αα+β|u|α−2u|v|β,x∈RN,−Δv−λ2v|x|2=a2|v|2*−2v+bh(x)βα+β|u|α|v|β−2v,x∈RN, where N ≥ 3,λ1,λ2 ∈ [0,ΛN), ΛN:=N−222 is the best Hardy constant. 2*=2NN−2 is the critical Sobolev exponent. a1,a2, b are positive parameters, α,β > 0 and 1 < α + β : = q < 2 < 2*. h(x)∈Lq′(RN) with q′=2*2*−q . By means of the concentration‐compactness principle and Kajikiya's new version of symmetric mountain pass lemma, we obtain infinitely many solutions that tend to zero for suitable positive parameters a1,a2,b and λ1,λ2. Copyright © 2012 John Wiley & Sons, Ltd.