We prove that if F is an element of C-1 (R) is coercive and {F' =0} is discrete, then the EFK equation u''' - c(2)u '' + F'(u) = 0 (1) possesses L-infinity(R) solutions if and only if F' changes sign at least twice. As a corollary we prove that if u(n) solves u(n)'''' + c(n)(2)u(n)'' + F'(u(n)) = 0, then parallel to u(n)parallel to(infinity) ->+infinity if c(n) ->0, provided F has a unique local minimum, its only minimum is nondegenerate and int({F' = 0}) = 0. Finally we give criteria ensuring existence and non-existence of T-periodic solutions to (1) when F has multiple wells. (C) 2013 Elsevier Inc. All rights reserved.