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December  2019, 39(12): 7141-7162. doi: 10.3934/dcds.2019299

## Predator-prey models with competition, Part Ⅲ: Classification of stationary solutions

 1 École des Hautes Études en Sciences Sociales, Centre d'analyse et de mathématique sociales (CAMS), CNRS, 54 bouvelard Raspail, 75006, Paris, France 2 Université Paris Diderot, Université de Paris, Laboratoire Jacques-Louis Lions (CNRS UMR 7598), 8 place Aurélie Nemours, 75205, Paris CEDEX 13, France

* Corresponding author: Henri Berestycki

To Luis Caffarelli, with admiration and affection

Received  December 2018 Revised  May 2019 Published  September 2019

For a stationary system representing prey and $N$ groups of competing predators, we show classification results about the set of positive solutions. In particular, we show that if the number of components $N$ is too large or if the competition between different groups is too small, then the system has only constant solutions, which we then completely characterize.

Citation: Henri Berestycki, Alessandro Zilio. Predator-prey models with competition, Part Ⅲ: Classification of stationary solutions. Discrete & Continuous Dynamical Systems, 2019, 39 (12) : 7141-7162. doi: 10.3934/dcds.2019299
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##### References:
Pictorial description of Theorem 1.1
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