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

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  • Yuangong Sun

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.

Suggested Citation

  • Yuangong Sun, 2011. "Oscillation of Certain Second-Order Sub-Half-Linear Neutral Impulsive Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-10, August.
    • Handle: RePEc:hin:jnddns:195619
    DOI: 10.1155/2011/195619
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