Nonexistence of single blow-up solutions for a nonlinear Schr"odinger equation involving critical Sobolev exponent

In this paper we consider the critical elliptic equation −Δu+λa(x)u=u(N+2)/(N−2), x∈RN,u>0, ∫RN|∇u|2dx<+∞,(1) where λ>0, N>4 and a(x) is a real continuous, nonnegative function, not identically zero. By using a local Pohozaev identity, we show that problem (1) does not admit a family of solutions uλ which blow up and concentrate as λ→+∞ at some zero point x0 of a(x) if the order of flatness of the function a(x) at x0 is β∈[2,N−4) and N≥