Abstract
A class of semilinear parabolic systems describing competing species is investigated with homogeneous Dirichlet or boundary conditions of the third kind; existence and attractivity properties of equilibrium solutions are proved by monotonicity methods. Attractive invariant subsets are shown to exist in a suitable function space, which in particular cases shrink down to a unique point. The outlined situation holds true even for a related class of parabolic integro-differential systems, provided the effect of the delay is small in a suitable sense.
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Schiaffino, A., Tesei, A. Competition systems with Dirichlet boundary conditions. J. Math. Biology 15, 93–105 (1982). https://doi.org/10.1007/BF00275791
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DOI: https://doi.org/10.1007/BF00275791