Sufficient conditions for the existence of non-oscillatory solutions to first-order differential equations with multiple advanced arguments
This article concerns the existence of non-oscillatory solutions to the equation $$ x'(t)=\sum_{k=1}^m a_k(t) x(h_k(t)), $$ where $a_k\geq 0$ and $h_k(t)\geq t$. We generalize existing results and then give an answer to the open question stated in [4]. Moreover we present a new condition...
| Main Author: | |
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| Format: | Article |
| Language: | English |
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Texas State University
2018-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/177/abstr.html |
| _version_ | 1819080293896683520 |
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| author | Julio G. Dix |
| author_facet | Julio G. Dix |
| author_sort | Julio G. Dix |
| collection | DOAJ |
| description | This article concerns the existence of
non-oscillatory solutions to the equation
$$
x'(t)=\sum_{k=1}^m a_k(t) x(h_k(t)),
$$
where $a_k\geq 0$ and $h_k(t)\geq t$.
We generalize existing results and then give an answer to the
open question stated in [4]. Moreover we present a new condition
based on the integral of $(\sum a_k)^2$. |
| first_indexed | 2024-12-21T19:42:35Z |
| format | Article |
| id | doaj.art-268660ef098047498ce53bcee2241746 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-21T19:42:35Z |
| publishDate | 2018-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-268660ef098047498ce53bcee22417462022-12-21T18:52:25ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912018-10-012018177,19Sufficient conditions for the existence of non-oscillatory solutions to first-order differential equations with multiple advanced argumentsJulio G. Dix0 Texas State Univ. San Marcos, TX, USA This article concerns the existence of non-oscillatory solutions to the equation $$ x'(t)=\sum_{k=1}^m a_k(t) x(h_k(t)), $$ where $a_k\geq 0$ and $h_k(t)\geq t$. We generalize existing results and then give an answer to the open question stated in [4]. Moreover we present a new condition based on the integral of $(\sum a_k)^2$.http://ejde.math.txstate.edu/Volumes/2018/177/abstr.htmlAdvanced linear differential equationpositive solutionoscillatory solution |
| spellingShingle | Julio G. Dix Sufficient conditions for the existence of non-oscillatory solutions to first-order differential equations with multiple advanced arguments Electronic Journal of Differential Equations Advanced linear differential equation positive solution oscillatory solution |
| title | Sufficient conditions for the existence of non-oscillatory solutions to first-order differential equations with multiple advanced arguments |
| title_full | Sufficient conditions for the existence of non-oscillatory solutions to first-order differential equations with multiple advanced arguments |
| title_fullStr | Sufficient conditions for the existence of non-oscillatory solutions to first-order differential equations with multiple advanced arguments |
| title_full_unstemmed | Sufficient conditions for the existence of non-oscillatory solutions to first-order differential equations with multiple advanced arguments |
| title_short | Sufficient conditions for the existence of non-oscillatory solutions to first-order differential equations with multiple advanced arguments |
| title_sort | sufficient conditions for the existence of non oscillatory solutions to first order differential equations with multiple advanced arguments |
| topic | Advanced linear differential equation positive solution oscillatory solution |
| url | http://ejde.math.txstate.edu/Volumes/2018/177/abstr.html |
| work_keys_str_mv | AT juliogdix sufficientconditionsfortheexistenceofnonoscillatorysolutionstofirstorderdifferentialequationswithmultipleadvancedarguments |