A singular Gierer–Meinhardt system of elliptic equations: the classical case Original Research Article

This paper studies the existence of solutions of a nonlinear elliptic system usually called the generalized Gierer–Meinhardt equations. This type of system originally arose in studies of pattern-formation in biology, and has interesting and challenging mathematical properties, especially with Dirichlet boundary conditions when the nonlinear terms become singular near the boundary. We study the existence of solutions in the classical case of Gierer–Meinhardt, when the activator-inhibitor model has different sources.