Sign changing solutions of the Brezis-Nirenberg problem in the hyperbolic space. (English) Zbl 1295.35203
This paper is concerned with the equivalent of the Brezis-Nirenberg problem for the critical Sobolev exponent on the hyperbolic space \({\mathbb B}^N\). The first main result establishes a nonexistence property if the parameter \(\lambda\) is at most \(N(N-2)/4\). Next, under certain values of \(\lambda\) and \(N\), the authors prove the existence of infinitely many nodal (that is, sign-changing) solutions as well as a compactness theorem for radial solutions. The proofs combine Sobolev embeddings, the Moser iteration and related estimates.
Reviewer: Vicenţiu D. Rădulescu (Craiova)
MSC:
| 35J20 | Variational methods for second-order elliptic equations |
| 35J60 | Nonlinear elliptic equations |
| 58E30 | Variational principles in infinite-dimensional spaces |
| 35B33 | Critical exponents in context of PDEs |
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