### 摘要

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.

原文 | English |
---|---|

頁（從 - 到） | 3211-3231 |

頁數 | 21 |

期刊 | Transactions of the American Mathematical Society |

卷 | 363 |

發行號 | 6 |

DOIs | |

出版狀態 | Published - 2011 六月 1 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

## 指紋 深入研究「Uniqueness of finite total curvatures and the structure of radial solutions for nonlinear elliptic equations」主題。共同形成了獨特的指紋。

## 引用此

Chern, J. L., Chen, Z. Y., & Tang, Y. L. (2011). Uniqueness of finite total curvatures and the structure of radial solutions for nonlinear elliptic equations.

*Transactions of the American Mathematical Society*,*363*(6), 3211-3231. https://doi.org/10.1090/S0002-9947-2011-05192-5