Monotonic Solutions of Second Order Nonlinear Difference Equations

Lianwen Wang, Anthony Willett

Abstract


Classification, boundedness, and existence of solutions of a second order nonlinear difference equation are investigated. First, it is proved that all  solutions are eventually monotone. Then, the necessary and sufficient conditions for the boundedness of all solutions are established. Finally, the existence of different types of monotonic solutions are presented. The obtained results have extended and improved some existing ones.


Keywords


Nonlinear difference equations; classification; bounded solutions; monotonic solutions

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