Abstract
We consider the following anisotropic Emden-Fowler equation with a singular source- div (a (x) ∇ v) = ε2 a (x) ev - 4 π α a (p) δp in Ω, v = 0 on ∂ Ω, where p ∈ Ω ⊂ R2, constant α ∈ (0, ∞) {set minus} 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 → 8 π (m + 1 + α) a (p).
| Original language | English |
|---|---|
| Pages (from-to) | 398-422 |
| Number of pages | 25 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 342 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jun 2008 |
Keywords
- Anisotropic Emden-Fowler equation
- Blowing-up solutions
- Singular source
- Variational reduction