In this work we prove the existence of solutions for an elliptic system between lower and upper solutions when the nonlinearities are Hölder continuous functions without a Lipschitz condition. Specifically, under appropriate conditions of monotony on the nonlinear reaction terms we introduce two monotone sequences which converge to a minimal and a maximal solution respectively. Finally, we apply these results to a dynamical population problem with "slow" diffusion.
"Existence of solutions for elliptic systems with Hölder continuous nonlinearities." Differential Integral Equations 13 (4-6) 453 - 477, 2000. https://doi.org/10.57262/die/1356061235