Blow-up analysis, existence and qualitative properties of solutions for the two-dimensional Emden–Fowler equation with singular potential
✍ Scribed by Daniele Bartolucci; Eugenio Montefusco
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 196 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.887
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✦ Synopsis
Abstract
Motivated by the study of a two‐dimensional point vortex model, we analyse the following Emden–Fowler type problem with singular potential:
where V(x) = K(x)/|x|^2α^ with α∈(0, 1), 0<a⩽K(x)⩽b< + ∞, ∀x∈Ω and ∥∇K∥~∞~⩽C. We first extend various results, already known in case α⩽0, to cover the case α∈(0, 1). In particular, we study the concentration‐compactness problem and the mass quantization properties, obtaining some existence results. Then, by a special choice of K, we include the effect of the angular momentum in the system and obtain the existence of axially symmetric one peak non‐radial blow‐up solutions. Copyright © 2007 John Wiley & Sons, Ltd.