### Abstract

We consider the scalar field equation -Δu(x)+(1|x|∗u2(x))u(x)-E2u(x)|x|+u(x) = 0 where u = u(|x|) is a radial positive solution and∗ is the convolution operator in R3. This equation can be rewritten as ordinary differential equation -ru"(r)-2u′(r)+r r∞(1s-1r)u2(s)s2dsu(r)+ru(r) = 0 and this note is concerned with asymptotic behavior at infinity of solutions of this equation.

Original language | English |
---|---|

Title of host publication | 39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013 |

Editors | George Venkov, Vesela Pasheva |

Publisher | American Institute of Physics Inc. |

Pages | 343-355 |

Number of pages | 13 |

Volume | 1570 |

ISBN (Electronic) | 9780735411685 |

DOIs | |

Publication status | Published - 2013 Jan 1 |

Externally published | Yes |

Event | 39th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2013 - Sozopol, Bulgaria Duration: 2013 Jun 8 → 2013 Jun 13 |

### Other

Other | 39th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2013 |
---|---|

Country | Bulgaria |

City | Sozopol |

Period | 13/6/8 → 13/6/13 |

### Keywords

- asymptotic behavior
- exponential integral
- Hartree equation
- solitary waves

### ASJC Scopus subject areas

- Physics and Astronomy(all)

## Fingerprint Dive into the research topics of 'Far field expansion for Hartree type equation'. Together they form a unique fingerprint.

## Cite this

Gueorguiev, V. S., & Venkov, G. (2013). Far field expansion for Hartree type equation. In G. Venkov, & V. Pasheva (Eds.),

*39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013*(Vol. 1570, pp. 343-355). American Institute of Physics Inc.. https://doi.org/10.1063/1.4854775