On positive solutions of some nonlinear differential equations - A probabilistic approach

Yuan-Chung Sheu*

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

By using connections between superdiffusions and partial differential equations (established recently by Dynkin, 1991), we study the structure of the set of all positive (bounded or unbounded) solutions for a class of nonlinear elliptic equations. We obtain a complete classification of all bounded solutions. Under more restrictive assumptions, we prove the uniqueness property of unbounded solutions, which was observed earlier by Cheng and Ni (1992).

Original languageEnglish
Pages (from-to)43-53
Number of pages11
JournalStochastic Processes and their Applications
Volume59
Issue number1
DOIs
StatePublished - 1 Jan 1995

Keywords

  • Branching particle systems
  • Measure-valued processes
  • Nonlinear elliptic equation
  • Range
  • Superdiffusions

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