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

Kimie Nakashima, Yoshio Yamada*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    33 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

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics


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