Oscillation of solutions of some generalized nonlinear α-difference equations
In this paper, the authors discuss the oscillation of solutions of some generalized nonlinear α-difference equation Δα(ℓ)(p(k)Δα(ℓ)u(k))+q(k)f(u(k−τ(k)))=0,(1) k∈[a,∞), where the functions p, q, f and τ are defined in their domain of definition and α>1, ℓ is a positive real. Further, uf(u)>0...
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| Format: | Article |
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SpringerOpen
2014
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| _version_ | 1825948519533379584 |
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| author | Manuel , Mariasebastin Maria Susai Kılıçman, Adem Srinivasan, K. Babu, G. Dominic |
| author_facet | Manuel , Mariasebastin Maria Susai Kılıçman, Adem Srinivasan, K. Babu, G. Dominic |
| author_sort | Manuel , Mariasebastin Maria Susai |
| collection | UPM |
| description | In this paper, the authors discuss the oscillation of solutions of some generalized nonlinear α-difference equation
Δα(ℓ)(p(k)Δα(ℓ)u(k))+q(k)f(u(k−τ(k)))=0,(1)
k∈[a,∞), where the functions p, q, f and τ are defined in their domain of definition and α>1, ℓ is a positive real. Further, uf(u)>0 for u≠0, p(k)>0 and limk→∞(k−τ(k))=∞, where Rk=∑[k−ℓℓ]r=01αrp(rℓ)→∞ as k→∞ and u(k) is defined for k≥mini≥0(i−τ(i)) for all k∈[a,∞) for some a∈[0,∞).
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| first_indexed | 2024-03-06T08:30:07Z |
| format | Article |
| id | upm.eprints-34793 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-03-06T08:30:07Z |
| publishDate | 2014 |
| publisher | SpringerOpen |
| record_format | dspace |
| spelling | upm.eprints-347932015-12-23T02:05:00Z http://psasir.upm.edu.my/id/eprint/34793/ Oscillation of solutions of some generalized nonlinear α-difference equations Manuel , Mariasebastin Maria Susai Kılıçman, Adem Srinivasan, K. Babu, G. Dominic In this paper, the authors discuss the oscillation of solutions of some generalized nonlinear α-difference equation Δα(ℓ)(p(k)Δα(ℓ)u(k))+q(k)f(u(k−τ(k)))=0,(1) k∈[a,∞), where the functions p, q, f and τ are defined in their domain of definition and α>1, ℓ is a positive real. Further, uf(u)>0 for u≠0, p(k)>0 and limk→∞(k−τ(k))=∞, where Rk=∑[k−ℓℓ]r=01αrp(rℓ)→∞ as k→∞ and u(k) is defined for k≥mini≥0(i−τ(i)) for all k∈[a,∞) for some a∈[0,∞). SpringerOpen 2014 Article PeerReviewed Manuel , Mariasebastin Maria Susai and Kılıçman, Adem and Srinivasan, K. and Babu, G. Dominic (2014) Oscillation of solutions of some generalized nonlinear α-difference equations. Advances in Difference Equations, 2014. art. no. 109. pp. 1-8. ISSN 1687-1839; ESSN: 1687-1847 http://www.advancesindifferenceequations.com/content/2014/1/109/abstract 10.1186/1687-1847-2014-109 |
| spellingShingle | Manuel , Mariasebastin Maria Susai Kılıçman, Adem Srinivasan, K. Babu, G. Dominic Oscillation of solutions of some generalized nonlinear α-difference equations |
| title | Oscillation of solutions of some generalized nonlinear α-difference equations |
| title_full | Oscillation of solutions of some generalized nonlinear α-difference equations |
| title_fullStr | Oscillation of solutions of some generalized nonlinear α-difference equations |
| title_full_unstemmed | Oscillation of solutions of some generalized nonlinear α-difference equations |
| title_short | Oscillation of solutions of some generalized nonlinear α-difference equations |
| title_sort | oscillation of solutions of some generalized nonlinear α difference equations |
| work_keys_str_mv | AT manuelmariasebastinmariasusai oscillationofsolutionsofsomegeneralizednonlinearadifferenceequations AT kılıcmanadem oscillationofsolutionsofsomegeneralizednonlinearadifferenceequations AT srinivasank oscillationofsolutionsofsomegeneralizednonlinearadifferenceequations AT babugdominic oscillationofsolutionsofsomegeneralizednonlinearadifferenceequations |