| Contents |
| We study qualitative properties of positive solutions of noncooperative, possibly nonvariational, elliptic systems such as
$$
\left\{ \begin{array}{rcl}
-\Delta u - \mu(x) u &=&u^r{\hskip 1pt}v^p\left[a(x)v^q-c(x)u^q\right] \\
-\Delta v - \nu(x) v &=&v^r{\hskip 1pt}u^p\left[b(x)u^q-d(x)v^q\right].
\end{array}
\right.
$$
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.
Arch. Rat. Mech. Anal. (2014), arXiv:1312.1380 |
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