## Abstract

This paper is concerned with the structure of the set of radially symmetric solutions for the equation{A formula is presented}with n > 2. Here the nonlinear term f is assumed to be a smooth function of u that is positive for u > 0 and is equal to 0 for u {less-than or slanted equal to} 0. Then any radial solution u = u ( r ), r = | x |, of the equation is shown to be classified into one of several types according to its behavior as r → 0 and r → ∞. Under the assumption that f is supercritical for small u > 0 and is subcritical for large u > 0, we clarify the entire structure of the set of solutions of various types. The Pohozaev identity plays a crucial role in the investigation of the structure.

Original language | English |
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Pages (from-to) | 440-463 |

Number of pages | 24 |

Journal | Journal of Differential Equations |

Volume | 224 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 May 15 |

Externally published | Yes |

## Keywords

- Elliptic equation
- Regular and singular solutions

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics