Existence of quasiperiodic solutions of elliptic equations on RN+1 via center manifold and KAM theorems

We consider elliptic equations on RN+1 of the form Delta(x)u + u(yy) + g(x, u) =0, (x, y) is an element of R-N x R where g(x, u) is a sufficiently regular function with g(., 0) 0. We give sufficient conditions for the existence of solutions of (1) which are quasiperiodic in y and decaying as vertical bar x vertical bar -> infinity uniformly in y. Such solutions are found using a center manifold reduction and results from the KAM theory. We discuss several classes of nonlinearities g to which our results apply. (C) 2017 Elsevier Inc. All rights reserved.