Positive solutions of elliptic systems with bounded nonlinearities
Ezzat S. Noussair, Charles A. Swanson · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1988
Synopsis Semilinear elliptic partial differential systems of second order with weak coupling are considered in exterior domains Ω ⊆ ℝN, N≧3. Conditions on the nonlinearities are given which guarantee the existence of solutions u with positive components in Ω such that u|∂Ω = 0 and u(x)→0 uniformly as |x|→∞. Asymptotic decay estimates for the solutions are established, including an exponential decay law under extra hypotheses.