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

Kimie Nakashima, Yoshio Yamada

    Research output: Contribution to journalArticle

    47 Citations (Scopus)

    Abstract

    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
    Volume1
    Issue number6
    Publication statusPublished - 1996

    Fingerprint

    Prey-predator Model
    Cross-diffusion
    Coexistence
    Nonlinear Elliptic Systems
    Fixed Point Index
    Lotka-Volterra Model
    Sufficient Conditions
    Existence of Positive Solutions
    Boundary value problems
    Uniqueness
    Boundary Value Problem
    Necessary Conditions

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Positive steady states for prey-predator models with cross-diffusion. / Nakashima, Kimie; Yamada, Yoshio.

    In: Advances in Differential Equations, Vol. 1, No. 6, 1996, p. 1099-1122.

    Research output: Contribution to journalArticle

    Nakashima, Kimie ; Yamada, Yoshio. / Positive steady states for prey-predator models with cross-diffusion. In: Advances in Differential Equations. 1996 ; Vol. 1, No. 6. pp. 1099-1122.
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