### 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 |
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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 |

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 |
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Country | Bulgaria |

City | Sozopol |

Period | 13/6/8 → 13/6/13 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*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

**Far field expansion for Hartree type equation.** / Gueorguiev, Vladimir Simeonov; Venkov, G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013.*vol. 1570, American Institute of Physics Inc., pp. 343-355, 39th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2013, Sozopol, Bulgaria, 13/6/8. https://doi.org/10.1063/1.4854775

}

TY - GEN

T1 - Far field expansion for Hartree type equation

AU - Gueorguiev, Vladimir Simeonov

AU - Venkov, G.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

KW - asymptotic behavior

KW - exponential integral

KW - Hartree equation

KW - solitary waves

UR - http://www.scopus.com/inward/record.url?scp=85061145838&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061145838&partnerID=8YFLogxK

U2 - 10.1063/1.4854775

DO - 10.1063/1.4854775

M3 - Conference contribution

VL - 1570

SP - 343

EP - 355

BT - 39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013

A2 - Venkov, George

A2 - Pasheva, Vesela

PB - American Institute of Physics Inc.

ER -