Existence and symmetric result for Liouville-Weyl fractional nonlinear Schr\'odinger equation
| Autor: | Torres, César |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study the existence of positive solution for the one dimensional Schr\"odinger equation with mixed Lioville-Weyl fractional derivatives \begin{eqnarray*}\label{Eq00} _{t}D_{\infty}^{\alpha}({_{-\infty}}D_{t}^{\alpha}u(t)) + V(t) u(t) = & f(u(t)),\;\;t\in \mathbb{R}\\ u\in H^{\alpha}(\mathbb{R}).\nonumber \end{eqnarray*} Furthermore, we analyse radial symmetry property of these solutions. The proof is carried out by using variational methods jointly with comparison and rearrangement argument. Comment: arXiv admin note: text overlap with arXiv:1308.4215; and text overlap with arXiv:1208.2545 by other authors without attribution |
| Databáze: | arXiv |
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