ABSTRACT
We concentrate now on the simplest case m = 2, N = 1, with the analytic cubic nonlinearity as in (132). We have seen a lot of non-L-S patterns (not min-max ones), but in the case of non-Lipschitz nonlinearities, i.e., for n > 0, we had no chance to verify their existence rigorously, because those patterns exhibit a complicated, oscillatory, and partially still unknown behavior close to finite interfaces. For the elliptic equation (132) in 1D (hence, for an ODE) admitting an-
alytic solutions, with no finite interfaces, we can explain how to do such a “linearized” matching (gluing together) of linearized oscillatory “tails” of various L-S patterns to get many non-L-S patterns.
