Abstract
We are concerned with the existence of blowing-up solutions to the following boundary value problem−Δu=λa(x)eu−4πNδ0 in Ω,u=0 on ∂Ω, where Ω is a smooth and bounded domain in R2 such that 0∈Ω, a(x) is a positive smooth function, N is a positive integer and λ>0 is a small parameter. Here δ0 defines the Dirac measure with pole at 0. We find conditions on the function a and on the domain Ω under which there exists a solution uλ blowing up at 0 and satisfying λ∫Ωa(x)euλ→8π(N+1) as λ→0+.
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