On the Semilinear Elliptic Equations (formula presented)

Jann Long Chern*, Yong Li Tang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we consider the semilinear elliptic equationΔu+β1+|x|μup-γ1+|x|νuqinRn,where n≥3, Δ=∑ni=1(∂2/∂x2i), 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 languageEnglish
Pages (from-to)27-38
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 2000 Apr 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'On the Semilinear Elliptic Equations (formula presented)'. Together they form a unique fingerprint.

Cite this