Higher order Schr\'odinger equations on hyperbolic spaces
| Autor: | Li, Jungang, Wang, Zhiwei |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study the following higher order Schr\"odinger equation on hyperbolic space $\mathbb{H}^n$: $P_m u +a(x) u = |u|^{q - 2}u,$ where $P_m$ is the $2m$ order GJMS operator, $q=\frac{2n}{n-2m}$, $a(x) \in L^{\frac{n}{2m}}(\mathbb{H}^n)$ is a nonnegative potential function. We obtain a new concentration compactness principal for higher order problems on hyperbolic spaces. Under certain integrability assumptions on $a(x)$, we obtain the existence of solutions of the Schr\"odinger equations. Comment: 42 pages |
| Databáze: | arXiv |
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