Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order
We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t)≔ri(t)ϕαixi-1Δ(t), i=1,…,n-1, with x0=x, ϕβ(u)≔uβsgnu, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous functi...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/6847956 |
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| author | Taher S. Hassan Said R. Grace |
| author_facet | Taher S. Hassan Said R. Grace |
| author_sort | Taher S. Hassan |
| collection | DOAJ |
| description | We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t)≔ri(t)ϕαixi-1Δ(t), i=1,…,n-1, with x0=x, ϕβ(u)≔uβsgnu, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous function such that limt→∞φi(t)=∞ for j=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations. |
| format | Article |
| id | doaj-art-0666aa6fce664301898a19ac94f03d22 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-0666aa6fce664301898a19ac94f03d222025-02-03T06:00:34ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/68479566847956Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher OrderTaher S. Hassan0Said R. Grace1Department of Mathematics, Faculty of Science, University of Hail, Hail 2440, Saudi ArabiaDepartment of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12221, EgyptWe will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t)≔ri(t)ϕαixi-1Δ(t), i=1,…,n-1, with x0=x, ϕβ(u)≔uβsgnu, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous function such that limt→∞φi(t)=∞ for j=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.http://dx.doi.org/10.1155/2016/6847956 |
| spellingShingle | Taher S. Hassan Said R. Grace Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order Discrete Dynamics in Nature and Society |
| title | Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order |
| title_full | Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order |
| title_fullStr | Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order |
| title_full_unstemmed | Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order |
| title_short | Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order |
| title_sort | comparison criteria for nonlinear functional dynamic equations of higher order |
| url | http://dx.doi.org/10.1155/2016/6847956 |
| work_keys_str_mv | AT tahershassan comparisoncriteriafornonlinearfunctionaldynamicequationsofhigherorder AT saidrgrace comparisoncriteriafornonlinearfunctionaldynamicequationsofhigherorder |