In:
Journal of Applied Mathematics, Wiley, Vol. 2012, No. 1 ( 2012-01)
Abstract:
We study the following second‐order super‐half‐linear impulsive differential equations with delay [ r ( t ) φ γ ( x ′ ( t ))] ′ + p ( t ) φ γ ( x ( t − σ )) + q ( t ) f ( x ( t − σ )) = e ( t ), t ≠ τ k , x ( t + ) = a k x ( t ), x ′ ( t + ) = b k x ′ ( t ), t = τ k , where t ≥ t 0 ∈ ℝ , φ * ( u ) = | u | *−1 u , σ is a nonnegative constant, { τ k } denotes the impulsive moments sequence with τ 1 〈 τ 2 〈 ⋯ 〈 τ k 〈 ⋯, lim k → ∞ τ k = ∞ , and τ k +1 − τ k 〉 σ . By some classical inequalities, Riccati transformation, and two classes of functions, we give several interval oscillation criteria which generalize and improve some known results. Moreover, we also give two examples to illustrate the effectiveness and nonemptiness of our results.
Type of Medium:
Online Resource
ISSN:
1110-757X
,
1687-0042
DOI:
10.1155/jama.v2012.1
Language:
English
Publisher:
Wiley
Publication Date:
2012
detail.hit.zdb_id:
2062866-3
detail.hit.zdb_id:
2578385-3
SSG:
17,1
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