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Monotone schemes for semilinear elliptic systems related to ecology
Author(s) -
Leung Anthony,
Rabinowitz P. H.
Publication year - 1982
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670040118
Subject(s) - mathematics , monotone polygon , uniqueness , partial differential equation , scalar (mathematics) , dirichlet boundary condition , dirichlet distribution , dirichlet problem , pure mathematics , boundary value problem , mathematical analysis , geometry
Semilinear elliptic systems of partial differential equations related to ecology are studied, with Dirichlet boundary conditions. Monotone sequences of functions which satisfy scalar equations are constructed so that they will converge to upper and lower bounds for the solutions of the systems. In case a related system has a unique positive solution, then these sequences will converge to the solution of the original system. Applications of the monotone sequences to uniqueness and stability are also given.