### Existence of solutions to recurrence relations

There are many open problems in this area. Here is one from the book by Kulenovic and Ladas.

A *solution *to the recurrence relation is a sequence of real numbers such that for all .

The existence problem for the recurrence relation is this: for which values of is there a solution of the recurrence relation with ?

References:

Kulenovic, M.R.S. & Ladas, G. (2002) Dynamics of second order rational difference equations. Chapman & Hall/CRC.

Camouzis, E., DeVault, R. & Lada, G. (2001) On the recursive sequence .* J. Diff Equations Applied*, vol 7.