Asymptotic properties of third order functional dynamic equations on time scales

I. Kubiaczyk, and S. H. Saker. "Asymptotic properties of third order functional dynamic equations on time scales." Annales Polonici Mathematici 100.3 (2011): 203-222. <http://eudml.org/doc/280758>.

@article{I2011,
abstract = {The purpose of this paper is to study the asymptotic properties of nonoscillatory solutions of the third order nonlinear functional dynamic equation $[p(t)[(r(t)x^\{Δ\}(t))^\{Δ\}]^\{γ\}]^\{Δ\} + q(t)f(x(τ(t))) = 0$, t ≥ t₀, on a time scale , where γ > 0 is a quotient of odd positive integers, and p, q, r and τ are positive right-dense continuous functions defined on . We classify the nonoscillatory solutions into certain classes $C_\{i\}$, i = 0,1,2,3, according to the sign of the Δ-quasi-derivatives and obtain sufficient conditions in order that $C_\{i\} = ∅$. Also, we establish some sufficient conditions which ensure the property A of the solutions. Our results are new for third order dynamic equations and involve and improve some results previously obtained for differential and difference equations. Some examples are worked out to demonstrate the main results.},
author = {I. Kubiaczyk, S. H. Saker},
journal = {Annales Polonici Mathematici},
keywords = {nonoscillatory solutions; time scale; third order dynamic equations},
language = {eng},
number = {3},
pages = {203-222},
title = {Asymptotic properties of third order functional dynamic equations on time scales},
url = {http://eudml.org/doc/280758},
volume = {100},
year = {2011},
}

TY - JOUR
AU - I. Kubiaczyk
AU - S. H. Saker
TI - Asymptotic properties of third order functional dynamic equations on time scales
JO - Annales Polonici Mathematici
PY - 2011
VL - 100
IS - 3
SP - 203
EP - 222
AB - The purpose of this paper is to study the asymptotic properties of nonoscillatory solutions of the third order nonlinear functional dynamic equation $[p(t)[(r(t)x^{Δ}(t))^{Δ}]^{γ}]^{Δ} + q(t)f(x(τ(t))) = 0$, t ≥ t₀, on a time scale , where γ > 0 is a quotient of odd positive integers, and p, q, r and τ are positive right-dense continuous functions defined on . We classify the nonoscillatory solutions into certain classes $C_{i}$, i = 0,1,2,3, according to the sign of the Δ-quasi-derivatives and obtain sufficient conditions in order that $C_{i} = ∅$. Also, we establish some sufficient conditions which ensure the property A of the solutions. Our results are new for third order dynamic equations and involve and improve some results previously obtained for differential and difference equations. Some examples are worked out to demonstrate the main results.
LA - eng
KW - nonoscillatory solutions; time scale; third order dynamic equations
UR - http://eudml.org/doc/280758
ER -