## Abstract

In this paper, we consider the semilinear elliptic equationΔu+β1+|x|^{μ}u^{p}-γ1+|x|^{ν}u^{q}inR^{n},where n≥3, Δ=∑^{n}_{i=1}(∂^{2}/∂x^{2}_{i}), β and γ are two positive constants, and p,q,μ,ν are constants with qp1 and μ≥ν2. We note that if β=0, γ0, and ν2, then the complete classification of all possible positive solutions was conducted by Cheng and Ni [Indiana Univ. Math. J.41 (1992), 261-278]. If γ=0 and β0, then (1.1) is the so-called Matukuma-type equation, and the solution structures were classified by Li and Ni [Duke Math. J.53 (1985), 895-924] and Ni and Yotsutani [Japan J. Appl. Math.5 (1988), 1-32]. If β0 and γ0, then some results about the structure of positive solutions of (1.1) were derived by the first author [Nonlinear Analysis, TM&A 28 (1997), 1741-1750]. The purpose of this paper is to discuss the uniqueness and properties of unbounded positive solutions and investigate some further structures of the positive solutions of Eq. (1.1).

Original language | English |
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Pages (from-to) | 27-38 |

Number of pages | 12 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 244 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2000 Apr 1 |

Externally published | Yes |

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics