On a homoclinic point of an autonomous second-order difference equation

Abstract

The paper deals with the second-order difference equation

where h>0 is a parameter and f has continuous first derivative and three zeros on the real line. The main result is that for each sufficiently small h the above equation has a homoclinic point.

Keywords:

• autonomous second-order difference equation
• homoclinic point
• strictly increasing solutions

Mathematics Subject Classification 2000::

• 39A11
• 39A12
• 39A70

Acknowledgements

The paper was supported by the Council of Czech Government MSM 6198959214. The authors thank the referees for their valuable comments.