Abstract
In this paper we establish the necessary and sufficient conditions for existence of solutions of the nonlinear two term difference equation
where
and
are regularly varying functions,
Also we obtain their asymptotic representations as
Since
and
could be more complicated than power functions and
for proving the main result we formulate and prove an additional statement about existence of vanishing solutions of quasilinear system of difference equations.
Notes
No potential conflict of interest was reported by the authors.