### Abstract

Exponential decay estimates are obtained for complex-valued solutions to nonlinear elliptic equations in ℝ^{n}, where the linear term is given by Schrödinger operators H = - Δ + V with nonnegative potentials V and the nonlinear term is given by a single power with subcritical Sobolev exponent in the attractive case. We describe specific rates of decay in terms of V, some of which are shown to be optimal. Moreover, our estimates provide a unified understanding of two distinct cases in the available literature, namely, the vanishing potential case V = 0 and the harmonic potential case V(x) = |x|^{2}.

Original language | English |
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Pages (from-to) | 1000-1011 |

Number of pages | 12 |

Journal | Zeitschrift fur Angewandte Mathematik und Physik |

Volume | 56 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2005 Nov 1 |

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### Keywords

- Bound states
- Exponential decay
- Nonlinear elliptic equations

### ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)
- Applied Mathematics