Positive steady states for prey-predator models with cross-diffusion

Kimie Nakashima, Yoshio Yamada

Research output: Contribution to journalArticlepeer-review

52 Citations (Scopus)


This paper is concerned with the existence of positive solutions for boundary value problems of nonlinear elliptic systems which arise in the study of the Lotka-Volterra prey-predator model with cross-diffusion. Making use of the theory of the fixed point index we can derive sufficient conditions for the coexistence of positive steady states. Moreover, when cross-diffusion effects are comparatively small, we can get a necessary and sufficient condition for the coexistence. The uniqueness result is also given in the special case when the spatial dimension is one.

Original languageEnglish
Pages (from-to)1099-1122
Number of pages24
JournalAdvances in Differential Equations
Issue number6
Publication statusPublished - 1996
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'Positive steady states for prey-predator models with cross-diffusion'. Together they form a unique fingerprint.

Cite this