Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2014

Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems

Résumé

We study qualitative properties of positive solutions of noncooperative, possibly nonvariational, elliptic systems. We obtain new classification and Liouville type theorems in the whole Euclidean space, as well as in half-spaces, and deduce a priori estimates and existence of positive solutions for related Dirichlet problems. We significantly improve the known results for a large class of systems involving a balance between repulsive and attractive terms. This class contains systems arising in biological models of Lotka-Volterra type, in physical models of Bose-Einstein condensates and in models of chemical reactions.
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Dates et versions

hal-00944637 , version 1 (10-02-2014)
hal-00944637 , version 2 (30-01-2015)

Identifiants

  • HAL Id : hal-00944637 , version 1

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Alexandre Montaru, Boyan Sirakov, Philippe Souplet. Proportionality of components, Liouville theorems and a priori estimates for noncooperative elliptic systems. 2014. ⟨hal-00944637v1⟩
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