Abstract
We establish the existence and uniqueness of a positive solution to the Schrödinger equation involving the fractional Laplacian \(\Delta ^{\frac{\alpha }{2}}u=\mu \,u\) in smooth bounded domains of \(\mathbb {R}^d\) for a large class of nonnegative perturbations \(\mu \). We then use this result to give some new facts about the fractional semilinear equation \(\Delta ^{\frac{\alpha }{2}}u= u^\gamma \), \(\gamma >0\).
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11 December 2017
We take this opportunity to correct some errors in Theorems 1, 2 and 3 of the original article. We keep the notations given in original article.
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A correction to this article is available online at https://doi.org/10.1007/s00009-017-1045-0.
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Chrouda, M.B. Fractional Schrödinger Equation in Bounded Domains and Applications. Mediterr. J. Math. 14, 172 (2017). https://doi.org/10.1007/s00009-017-0972-0
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DOI: https://doi.org/10.1007/s00009-017-0972-0