Monotone schemes for semilinear elliptic systems related to ecology
Anthony W. Leung, Paul H. Rabinowitz · Mathematical Methods in the Applied Sciences · 1982
Abstract 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.