Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term

Hassan, Taher S.. "Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term." Serdica Mathematical Journal 34.4 (2008): 715-732. <http://eudml.org/doc/281457>.

@article{Hassan2008,
abstract = {2000 Mathematics Subject Classification: 34C10, 34C15.It is the purpose of this paper to give oscillation criteria for the second order nonlinear differential equation with a damping term (a(t) y′(t))′ + p(t)y′(t) + q(t) |y(t)| α−1 y(t) = 0, t ≥ t0, where α ≥ 1, a ∈ C1([t0,∞);(0,∞)) and p,q ∈ C([t0,∞);R). Our results here are different, generalize and improve some known results for oscillation of second order nonlinear differential equations that are different from most known ones in the sencse they are based on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line and can be applied to extreme cases such as ∫t0∞ q(t) dt = − ∞. Our results are illustrated with an example.},
author = {Hassan, Taher S.},
journal = {Serdica Mathematical Journal},
keywords = {Interval Oscillation; Second Order; Nonlinear Differential Equations; oscillation criteria; second-order nonlinear differential equation; damping term},
language = {eng},
number = {4},
pages = {715-732},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term},
url = {http://eudml.org/doc/281457},
volume = {34},
year = {2008},
}

TY - JOUR
AU - Hassan, Taher S.
TI - Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term
JO - Serdica Mathematical Journal
PY - 2008
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 34
IS - 4
SP - 715
EP - 732
AB - 2000 Mathematics Subject Classification: 34C10, 34C15.It is the purpose of this paper to give oscillation criteria for the second order nonlinear differential equation with a damping term (a(t) y′(t))′ + p(t)y′(t) + q(t) |y(t)| α−1 y(t) = 0, t ≥ t0, where α ≥ 1, a ∈ C1([t0,∞);(0,∞)) and p,q ∈ C([t0,∞);R). Our results here are different, generalize and improve some known results for oscillation of second order nonlinear differential equations that are different from most known ones in the sencse they are based on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line and can be applied to extreme cases such as ∫t0∞ q(t) dt = − ∞. Our results are illustrated with an example.
LA - eng
KW - Interval Oscillation; Second Order; Nonlinear Differential Equations; oscillation criteria; second-order nonlinear differential equation; damping term
UR - http://eudml.org/doc/281457
ER -