Sign changing solutions of the Brezis-Nirenberg problem in the hyperbolic space (Q2248841)

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.