Existence of solutions for elliptic systems with Hölder continuous nonlinearities

Abstract

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.