Let 0 R N be any open set. We study the nonlinear eigenvalue problem &2 p u =\*V(x) |u| p&2 u, u # D 1, p 0 (0), where 1<p<N and V # L 1 loc (0) may have strong singularities and an indefinite sign. The key ingredient is a precised concentrationcompactness lemma related to V-dependent limiting probl
✦ LIBER ✦
Critical singular problems via concentration-compactness lemma
✍ Scribed by Ronaldo B. Assunção; Paulo Cesar Carrião; Olimpio Hiroshi Miyagaki
- Book ID
- 108175537
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 207 KB
- Volume
- 326
- Category
- Article
- ISSN
- 0022-247X
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In this paper we study the existence of critical points of the functional where 0 # R d , d 2 is a bounded domain with C 3 boundary, u # H 1 (0), and = is a small parameter. On the nonlinearity F we assume: ). Additionally we require that there exists q>1 such that for u>0 the function F$(u)Âu q i