Oscillation of solutions to third-order half-linear neutral differential equations
In this article, we study the oscillation of solutions to the third-order neutral differential equations $$ Big(a(t)ig([x(t)pm p(t)x(delta(t))]''ig)^alphaBig)' + q(t)x^alpha(au(t)) = 0. $$ Sufficient conditions are established so that every solution is either oscillatory or con...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2012-02-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/29/abstr.html |
| _version_ | 1818754174721982464 |
|---|---|
| author | Jozef Dzurina Ethiraju Thandapani Sivaraj Tamilvanan |
| author_facet | Jozef Dzurina Ethiraju Thandapani Sivaraj Tamilvanan |
| author_sort | Jozef Dzurina |
| collection | DOAJ |
| description | In this article, we study the oscillation of solutions to the third-order neutral differential equations $$ Big(a(t)ig([x(t)pm p(t)x(delta(t))]''ig)^alphaBig)' + q(t)x^alpha(au(t)) = 0. $$ Sufficient conditions are established so that every solution is either oscillatory or converges to zero. In particular, we extend the results obtain in [1] for $a(t)$ non-decreasing, to the non-increasing case. |
| first_indexed | 2024-12-18T05:19:04Z |
| format | Article |
| id | doaj.art-5c78d12201b94f729304cbc4bb236d89 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T05:19:04Z |
| publishDate | 2012-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-5c78d12201b94f729304cbc4bb236d892022-12-21T21:19:43ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-02-01201229,19Oscillation of solutions to third-order half-linear neutral differential equationsJozef DzurinaEthiraju ThandapaniSivaraj TamilvananIn this article, we study the oscillation of solutions to the third-order neutral differential equations $$ Big(a(t)ig([x(t)pm p(t)x(delta(t))]''ig)^alphaBig)' + q(t)x^alpha(au(t)) = 0. $$ Sufficient conditions are established so that every solution is either oscillatory or converges to zero. In particular, we extend the results obtain in [1] for $a(t)$ non-decreasing, to the non-increasing case.http://ejde.math.txstate.edu/Volumes/2012/29/abstr.htmlThird-order neutral differential equationRiccati transformationoscillation of solutions |
| spellingShingle | Jozef Dzurina Ethiraju Thandapani Sivaraj Tamilvanan Oscillation of solutions to third-order half-linear neutral differential equations Electronic Journal of Differential Equations Third-order neutral differential equation Riccati transformation oscillation of solutions |
| title | Oscillation of solutions to third-order half-linear neutral differential equations |
| title_full | Oscillation of solutions to third-order half-linear neutral differential equations |
| title_fullStr | Oscillation of solutions to third-order half-linear neutral differential equations |
| title_full_unstemmed | Oscillation of solutions to third-order half-linear neutral differential equations |
| title_short | Oscillation of solutions to third-order half-linear neutral differential equations |
| title_sort | oscillation of solutions to third order half linear neutral differential equations |
| topic | Third-order neutral differential equation Riccati transformation oscillation of solutions |
| url | http://ejde.math.txstate.edu/Volumes/2012/29/abstr.html |
| work_keys_str_mv | AT jozefdzurina oscillationofsolutionstothirdorderhalflinearneutraldifferentialequations AT ethirajuthandapani oscillationofsolutionstothirdorderhalflinearneutraldifferentialequations AT sivarajtamilvanan oscillationofsolutionstothirdorderhalflinearneutraldifferentialequations |