Singular Elliptic Problems with Critical Sobolev-Hardy Exponents in RN

摘要

Let N ≥3 , λ＞ 0 , 2 ＜ q ＜ 2* = 2N/N-2, 0≤s＜2,0≤μ＜(N-2/2)2 and 2*(s) = 2(N-s)/N-2 be the critical Sobolev-Hardy exponents . Via the variational methods and analytic technique, we prove the existence of nontrivial solutions to the singular semilinear problem -△u-μ u/|x|u = |u|2*(s)-2/|x|s u+λ|u|q-2 u,u∈H1(RN).