Singular elliptic problems with lack of compactness
✍ Scribed by Marius Ghergu; Vicenţiu Rădulescu
- Book ID
- 106299330
- Publisher
- Springer
- Year
- 2005
- Tongue
- English
- Weight
- 307 KB
- Volume
- 185
- Category
- Article
- ISSN
- 0373-3114
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📜 SIMILAR VOLUMES
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
## Abstract We study a class of time‐independent non‐linear Schrödinger‐type equations on the whole space with a repulsive singular potential in the divergence operator and we establish the existence of non‐trivial standing wave solutions for this problem in an appropriate weighted Sobolev space. S