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

Jann Long Chern, Zhi You Chen, Yong Li Tang

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)3211-3231
Number of pages21
JournalTransactions of the American Mathematical Society
Volume363
Issue number6
DOIs
Publication statusPublished - 2011 Jun 1

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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