HETEROCLINIC ORBITS FOR A HIGHER-ORDER PHASE-TRANSITION PROBLEM

A standard model for one-dimensional phase transitions is the second-o rder semilinear equation with bistable nonlinearity, where one seeks a solution which connects the two stable values. From an Ising-like mod el but which includes long-range interaction, one is led to consider t he equation where the second-order operator is replaced by one of arbi trarily high order. Others have found the desired heteroclinic solutio ns for such equations, under the assumption that the higher-order term s have small coefficients, by employing singular perturbation methods for dynamical systems. Here, without making any assumption on the size s of the coefficients, we obtain such heteroclinic solutions by using variational methods under the assumption that the nonlinearity arises from a potential having two wells of equal depths.