### Abstract

We study global uniqueness in an inverse problem for the fractional semilinear Schrödinger equation (-Δ)su + q(x, u) = 0 with s ε (0, 1). We show that an unknown function q(x, u) can be uniquely determined by the Cauchy data set. In particular, this result holds for any space dimension greater than or equal to 2. Moreover, we demonstrate the comparison principle and provide an L ^{∞} estimate for this nonlocal equation under appropriate regularity assumptions.

Original language | English (US) |
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Pages (from-to) | 1189-1199 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 147 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2019 |

### Keywords

- Calderón’s problem
- Fractional schrödinger equation
- Maximum principle
- Nonlocal
- Partial data
- Semilinear

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## Cite this

Lai, R. Y., & Lin, Y. H. (2019). Global uniqueness for the fractional semilinear schrödinger equation.

*Proceedings of the American Mathematical Society*,*147*(3), 1189-1199. https://doi.org/10.1090/proc/14319