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## Poincar\'{e} Sobolev equations in the Hyperbolic space

### Abstract

We study the a priori estimates,existence/nonexistence of radial sign changing solution, and the Palais-Smale characterisation of the problem $-\De_{\Bn}u - \la u = |u|^{p-1}u, u\in H^1(\Bn)$ in the hyperbolic space $\Bn$ where $1<p\leq\frac{N+2}{N-2}$. We will also prove the existence of sign changing solution to the Hardy-Sobolev-Mazya equation and the critical Grushin problem

Topics: Mathematics - Analysis of PDEs, 35J60(primary), 35A15, 58j05 (secondary)
Year: 2011
OAI identifier: oai:arXiv.org:1103.4779