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)δp in Ω, v =0 on∂Ω, where p ∈ Ω ⊂ R2, constant α ∈ (0,∞) \ N, a(x) is a positive smooth function and δp denotes the Dirac measure with pole at point p. If p is a local maximum point of a(x), we construct a family of solutions vε with arbitrary m bubbles concentrating at p, and the quantity ε2 Ω a(x)evε →8π(m+1+ α)a(p). © 2007 Elsevier Inc. All rights reserved.