Abstract and Applied Analysis

Nonoscillation of Second-Order Dynamic Equations with Several Delays

Elena Braverman and Başak Karpuz

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Abstract

Existence of nonoscillatory solutions for the second-order dynamic equation ( A 0 x Δ ) Δ ( t ) + i [ 1 , n ] A i ( t ) x ( α i ( t ) ) = 0 for t [ t 0 , ) 𝕋 is investigated in this paper. The results involve nonoscillation criteria in terms of relevant dynamic and generalized characteristic inequalities, comparison theorems, and explicit nonoscillation and oscillation conditions. This allows to obtain most known nonoscillation results for second-order delay differential equations in the case A 0 ( t ) 1 for t [ t 0 , ) and for second-order nondelay difference equations ( α i ( t ) = t + 1 for t [ t 0 , ) ). Moreover, the general results imply new nonoscillation tests for delay differential equations with arbitrary A 0 and for second-order delay difference equations. Known nonoscillation results for quantum scales can also be deduced.

Article information

Source
Abstr. Appl. Anal., Volume 2011, Number 1 (2011), Article ID 591254, 34 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171400

Digital Object Identifier
doi:10.1155/2011/591254

Mathematical Reviews number (MathSciNet)
MR2793776

Zentralblatt MATH identifier
1217.34139

Citation

Braverman, Elena; Karpuz, Başak. Nonoscillation of Second-Order Dynamic Equations with Several Delays. Abstr. Appl. Anal. 2011 (2011), no. 1, Article ID 591254, 34 pages. doi:10.1155/2011/591254. https://projecteuclid.org/euclid.aaa/1313171400


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