Abstract
Motivated by some results of L. Berg (2002), in this paper we find the second member in the asymptotic development of some of the positive solutions of a class of difference equations of second and third orders. The main result in this paper partially solves an open problem by S. Stević (2003), and it is applied to some classes of mathematical biology models, for example, generalized Beverton‐Holt stock recruitment model, flour beetle population model, mosquito population equations, and discrete delay logistic difference equation.
Highlights
There has been a great interest in studying nonlinear difference equations and systems
One of the reasons for this is a necessity for some techniques which can be used in investigating equations arising in mathematical models describing real-life situations in population biology, economy, probability theory, genetics, psychology, sociology, and so forth
There are sequences defined by recurrence formulae such that we know their asymptotic behavior, see, for example, [11, 12, 14, 15, 19, 21, 23, 29, 30, 32, 33, 36], that is, we know the first member in their asymptotic behavior
Summary
Berg (2002), in this paper we find the second member in the asymptotic development of some of the positive solutions of a class of difference equations of second and third orders. The main result in this paper partially solves an open problem by S. Stevic (2003), and it is applied to some classes of mathematical biology models, for example, generalized Beverton-Holt stock recruitment model, flour beetle population model, mosquito population equations, and discrete delay logistic difference equation
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