Abstract

In this work we construct a family of entire bounded solutions for the singularly perturbed inhomogeneous Allen-Cahn equation epsilon(2) div(a(x)del u) - a(x)F' (u) = 0 in R-2, where epsilon -> 0. The nodal set of these solutions is close to a nondegenerate curve which is asymptotically two non-parallel straight lines. Here F' is a double-well potential and a is a smooth positive function. We also provide example of curves and functions a where our result applies. This work is in connection with the results found in [7,5,10] handling the compact case. (C) 2013 Elsevier Inc. All rights reserved.