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2011 Nonoscillation of Second-Order Dynamic Equations with Several Delays
Elena Braverman, Başak Karpuz
Abstr. Appl. Anal. 2011(SI1): 1-34 (2011). DOI: 10.1155/2011/591254


Existence of nonoscillatory solutions for the second-order dynamic equation (A0xΔ)Δ(t)+i[1,n]Ai(t)x(αi(t))=0 for t[t0,)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 A0(t)1 for t[t0,) and for second-order nondelay difference equations (αi(t)=t+1 for t[t0,)). Moreover, the general results imply new nonoscillation tests for delay differential equations with arbitrary A0 and for second-order delay difference equations. Known nonoscillation results for quantum scales can also be deduced.


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Elena Braverman. Başak Karpuz. "Nonoscillation of Second-Order Dynamic Equations with Several Delays." Abstr. Appl. Anal. 2011 (SI1) 1 - 34, 2011.


Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1217.34139
MathSciNet: MR2793776
Digital Object Identifier: 10.1155/2011/591254

Rights: Copyright © 2011 Hindawi

Vol.2011 • No. SI1 • 2011
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