| This paper studies the following semilinear elliptic equation: where a smooth bounded domain, ai∈Ω, (i=1,2,..,k)are different points, is the best Hardy constant, 2* = 2N /(N-2)is the critical Sobolev exponent.In this paper,we establish the local Palais-Smale condition, then prove the existence of sign-changing solutions to the semilinear elliptic equation involving critical Sobolev exponent and Hardy-type term using the variational principles and the Mountain Pass Theorem and the asymptotic behavior of non-trivial solutions to the equation at the singular point by employing Moser. |
