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

Serdica Mathematical Journal (2008)

- Volume: 34, Issue: 4, page 715-732
- ISSN: 1310-6600

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topHassan, 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 -

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