Difference analogue of the Lemma on the Logarithmic Derivative with   applications to difference equations
  The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is presented and then applied to prove a number of results on meromorphic solutions of complex difference equations. These results include a difference analogue of the Clunie Lemma, as well as other results on the value distribution of solutions. 
R. G. Halburd and R. J. Korhonen