Nonoscillation of Second-Order Dynamic Equations with Several Delays
Existence of nonoscillatory solutions for the second-order dynamic equation (A0xΔ)Δ(t)+∑i∈[1,n]ℕAi(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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/591254 |
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| Summary: | Existence of nonoscillatory solutions for the second-order dynamic equation (A0xΔ)Δ(t)+∑i∈[1,n]ℕAi(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,∞)R and for second-order nondelay difference equations (αi(t)=t+1 for t∈[t0,∞)N). 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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| ISSN: | 1085-3375 1687-0409 |