| For a singularly perturbed system with one-dimensional spatial domain, we present a method to construct solutions with multiple internal and boundary layers. Using Melnikov's method, we show that the distances between the layers are inversely proportional to the weakest eigenvalues of the Jacobian matrices associated to the equilibria of the system. A system of bifurcation functions is derived by a Lyapunov-Schmidt procedure and is solved using degree theory. The method was previously used to treat Silnikov-type bifurcation problems defined on the entire real axis (29). It is adapted to treat internal layer problems on a finite interval for the first time. |
