Blowing-up solutions to an anisotropic Emden–Fowler equation with a singular source

We consider the following anisotropic Emden–Fowler equation with a singular source−div(a(x)∇v)=ε2a(x)ev−4παa(p)δpin Ω,v=0on ∂Ω, where p∈Ω⊂R2p∈Ω⊂R2, constant α∈(0,∞)∖Nα∈(0,∞)∖N, a(x)a(x) is a positive smooth function and δpδp denotes the Dirac measure with pole at point p. If p   is a local maximum point of a(x)a(x), we construct a family of solutions vεvε with arbitrary m bubbles concentrating at p  , and the quantity ε2∫Ωa(x)evε→8π(m+1+α)a(p)ε2∫Ωa(x)evε→8π(m+1+α)a(p).