### Abstract

In this article, we are concerned with the semilinear elliptic equation δu + K(|x|)|u|^{p-1}u = 0 in R^{n} \ {0}, where n > 2, p > 1, and K(|x|) > 0 in R^{n}. The correspondence between the initial values of regularly positive radial solutions of the above equation and the associated finite total curvatures will be derived. In addition, we also conduct the zeros of radial solutions in terms of the initial data under specific conditions on K and p. Furthermore, based on the Pohozaev identity and openness for the regions of initial data corresponding to certain types of solutions, we obtain the whole structure of radial solutions depending on various situations.

Original language | English |
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Pages (from-to) | 3211-3231 |

Number of pages | 21 |

Journal | Transactions of the American Mathematical Society |

Volume | 363 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2011 Jun 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*363*(6), 3211-3231. https://doi.org/10.1090/S0002-9947-2011-05192-5

}

*Transactions of the American Mathematical Society*, vol. 363, no. 6, pp. 3211-3231. https://doi.org/10.1090/S0002-9947-2011-05192-5

**Uniqueness of finite total curvatures and the structure of radial solutions for nonlinear elliptic equations.** / Chern, Jann Long; Chen, Zhi You; Tang, Yong Li.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Uniqueness of finite total curvatures and the structure of radial solutions for nonlinear elliptic equations

AU - Chern, Jann Long

AU - Chen, Zhi You

AU - Tang, Yong Li

PY - 2011/6/1

Y1 - 2011/6/1

N2 - In this article, we are concerned with the semilinear elliptic equation δu + K(|x|)|u|p-1u = 0 in Rn \ {0}, where n > 2, p > 1, and K(|x|) > 0 in Rn. The correspondence between the initial values of regularly positive radial solutions of the above equation and the associated finite total curvatures will be derived. In addition, we also conduct the zeros of radial solutions in terms of the initial data under specific conditions on K and p. Furthermore, based on the Pohozaev identity and openness for the regions of initial data corresponding to certain types of solutions, we obtain the whole structure of radial solutions depending on various situations.

AB - In this article, we are concerned with the semilinear elliptic equation δu + K(|x|)|u|p-1u = 0 in Rn \ {0}, where n > 2, p > 1, and K(|x|) > 0 in Rn. The correspondence between the initial values of regularly positive radial solutions of the above equation and the associated finite total curvatures will be derived. In addition, we also conduct the zeros of radial solutions in terms of the initial data under specific conditions on K and p. Furthermore, based on the Pohozaev identity and openness for the regions of initial data corresponding to certain types of solutions, we obtain the whole structure of radial solutions depending on various situations.

UR - http://www.scopus.com/inward/record.url?scp=79952138358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952138358&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2011-05192-5

DO - 10.1090/S0002-9947-2011-05192-5

M3 - Article

AN - SCOPUS:79952138358

VL - 363

SP - 3211

EP - 3231

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 6

ER -