Steady state solutions for a general activator–inhibitor model

We discuss existence results for a singular Gierer–Meinhardt elliptic system with zero Dirichlet boundary conditions, which originally arose in studies of pattern-formation in biology and has interesting and challenging mathematical properties. The mathematical difficulties are that the system becomes singular near the boundary and it is non-quasimonotone. We show the existence of positive solutions for the general activator–inhibitor model.