Oscillation of Certain Second-Order Sub-Half-Linear Neutral Impulsive Differential Equations

Yuangong Sun

Discrete Dynamics in Nature and Society, 2011, vol. 2011, 1-10

Abstract:

By introducing auxiliary functions, we investigate the oscillation of a class of second-order sub-half-linear neutral impulsive differential equations of the form [ r ( t ) ϕ β ( z ′ ( t ) ) ] ′ + p ( t ) ϕ α ( x ( σ ( t ) ) ) = 0 ,   t ≠θ k , Δ ϕ β ( z ′ ( t ) ) | t = θ k + q k ϕ α ( x ( σ ( θ k ) ) ) = 0 , Δ x ( t ) | t = θ k = 0 , where β > α > 0 ,   z ( t ) = x ( t ) + λ ( t ) x ( τ ( t ) ) .     Several oscillation criteria for the above equation are established in both the case 0 ≤ λ ( t ) ≤ 1 and the case - 1 < - μ ≤ λ ( t ) ≤ 0 , which generalize and complement some existing results in the literature. Two examples are also given to illustrate the effect of impulses on the oscillatory behavior of solutions to the equation.

Date: 2011
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2011/195619.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2011/195619.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:195619

DOI: 10.1155/2011/195619

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().