Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
841123 | Nonlinear Analysis: Theory, Methods & Applications | 2010 | 11 Pages |
Abstract
This article is concerned with the effect of different types of competitive interaction terms on the large-interaction limit of nonlinear elliptic systems modelling the steady states of populations that compete in some region. As the competition rate tends to infinity, we show that non-negative solutions of quite simple-looking systems converge to the positive and negative parts of a solution of a scalar limit problem which may be much more strongly nonlinear than the original system, possibly with quadratic growth in the gradient of the limit function.
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Authors
E.C.M. Crooks, E.N. Dancer,