The solution gap of the Brezis-Nirenberg problem on the hyperbolic space
| Autor: | Benguria, Soledad |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00605-015-0861-1 |
| Popis: | We consider the positive solutions of the nonlinear eigenvalue problem $-\Delta_{\mathbb{H}^n} u = \lambda u + u^p, $ with $p=\frac{n+2}{n-2}$ and $u \in H_0^1(\Omega),$ where $\Omega$ is a geodesic ball of radius $\theta_1$ on $\mathbb{H}^n.$ For radial solutions, this equation can be written as an ODE having $n$ as a parameter. In this setting, the problem can be extended to consider real values of $n.$ We show that if $2 Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00605-015-0861-1 |
| Databáze: | arXiv |
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