Department of Mathematics, Faculty of Science, Palacký University, tř. 17. listopadu 12, 77146 Olomouc, Czech Republic
Copyright © 2010 Lukáš Rachůnek and Irena Rachůnková. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The paper provides conditions sufficient for the existence of strictly increasing solutions of the second-order nonautonomous difference equation , , where is a parameter and is Lipschitz continuous and has three real zeros . In particular we prove that for each sufficiently small there exists a solution such that is increasing, and . The problem is motivated by some models arising in hydrodynamics.