Positive solutions of certain nonlinear elliptic systems with self-diffusions: nondegenerate vs. degenerate diffusions Original Research Article

We discuss the existence of positive solutions to certain strongly-coupled nonlinear elliptic systems with self-diffusions under homogeneous Dirichlet boundary conditions. Using the global positive coexistence results for predator–prey, competition and symbiotic interactions between two species, sufficient conditions for the positive solutions of the degenerate self-diffusive systems are studied. We also investigate the local behavior, namely, the local existence, uniqueness and stability, of positive solutions for predator–prey and competition interactions. Our method is based on the decoupling technique and bifurcation theory.