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Since q ( t ) > 0, every eventually positive solution of (2) is nondecreasing for large t.
Conditions under which every eventually positive solution belongs to one of three mutually distinct sets are derived.
Moreover, is a recessive solution, is a dominant solution, and every eventually positive solution of (1.1) is normalized regularly varying, with.
If conditions (7 - 9) and (14) are satisfied, every eventually non-oscillatory solution (X=X(n)), (ninmathbb{Z}_{n_{0}-eta}^{infty}) of (1) fulfilling condition (III) is bounded.
If conditions (7 - 9) and (14) are satisfied, then every eventually non-oscillatory solution (X=X(n)), (ninmathbb{Z}_{n_{0}-eta}^{infty}) of (1) fulfilling one of conditions (I), (II) is unbounded.
In the following theorem, we give all possibilities for the signs of components of every eventually non-oscillatory solution (X=X(n)), (ninmathbb{Z}_{n_{0}-eta}^{infty}) of the system (1).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com