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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| Format: | Article |
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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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| author | Elena Braverman Başak Karpuz |
| author_facet | Elena Braverman Başak Karpuz |
| author_sort | Elena Braverman |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ef86d8363e904e04be2c08f9ca4560ef |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ef86d8363e904e04be2c08f9ca4560ef2025-08-20T03:21:13ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/591254591254Nonoscillation of Second-Order Dynamic Equations with Several DelaysElena Braverman0Başak Karpuz1Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, CanadaDepartment of Mathematics, Faculty of Science and Arts, ANS Campus, Afyon Kocatepe University, 03200 Afyonkarahisar, TurkeyExistence 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.http://dx.doi.org/10.1155/2011/591254 |
| spellingShingle | Elena Braverman Başak Karpuz Nonoscillation of Second-Order Dynamic Equations with Several Delays Abstract and Applied Analysis |
| title | Nonoscillation of Second-Order Dynamic Equations with Several Delays |
| title_full | Nonoscillation of Second-Order Dynamic Equations with Several Delays |
| title_fullStr | Nonoscillation of Second-Order Dynamic Equations with Several Delays |
| title_full_unstemmed | Nonoscillation of Second-Order Dynamic Equations with Several Delays |
| title_short | Nonoscillation of Second-Order Dynamic Equations with Several Delays |
| title_sort | nonoscillation of second order dynamic equations with several delays |
| url | http://dx.doi.org/10.1155/2011/591254 |
| work_keys_str_mv | AT elenabraverman nonoscillationofsecondorderdynamicequationswithseveraldelays AT basakkarpuz nonoscillationofsecondorderdynamicequationswithseveraldelays |