Abstract
This paper investigates the existence of positive strongly decaying solutions of second-order nonlinear q-difference equation
with q-regularly varying coefficients a and b. By means of a fixed point theorem in partially ordered Banach space, necessary and sufficient conditions for the existence of solutions satisfying
and
as
are established. Moreover, with the help of q-regular varying theory, precise asymptotic behaviour of such solutions is described.
Acknowledgments
Authors would like to express their sincere thanks to referees for a number of useful comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 .