王征平; 周焕松
Wang Zhengping; Zhou Huansong
摘要:
For the following elliptic problem
-△ u - μu/|x|2={|u|2*(s)-2u}/|x|s+h(x), on RN
u ∈ D1,2(RN), N≥3, 0≤μ<\bar\mu=(N-2)2 /4, 0≤ s<2,
where 2*(s)=2(N-s)/(N-2) is the critical Sobolev-Hardy exponent, h(x)∈ D1,2(RN))* , the dual space of (D1,2(RN)), with h(x)≥(≠) 0. By Ekeland's variational principle, subsuper solutions and a Mountain Pass theorem, the authors prove that the above problem has at least two distinct solutions if
||h||*
CN,s=(4-2s)/(N-2) ((N-2)/(N+2-2s)(N+2-2s)/(4-2s)
and As=inf u∈ D1,2(RN)\{0} {∫RN(|▽u|2-μu2/|x|2) dx}/{(∫RN|u|2*(s)/|x|s dx)2/2*(s)}.
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