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

Yuan-Chung Sheu

Stochastic Processes and their Applications, 1995, vol. 59, issue 1, 43-53

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).

Keywords: Branching; particle; systems; Measure-valued; processes; Nonlinear; elliptic; equation; Range; Superdiffusions (search for similar items in EconPapers)
Date: 1995
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