Modified Riccati technique for half-linear differential equations with delay
We study the half-linear differential equation $$ (r(t)\Phi(x'(t)))'+c(t)\Phi(x(\tau(t)))=0,\quad \Phi(x):=|x|^{p-2}x,\ p>1. $$ We formulate new oscillation criteria for this equation by comparing it with a certain ordinary linear or half-linear differential equation. Our proofs are b...
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| Format: | Article |
| Language: | English |
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University of Szeged
2014-12-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3344 |
| _version_ | 1797830612745191424 |
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| author | Simona Fišnarová Robert Marik |
| author_facet | Simona Fišnarová Robert Marik |
| author_sort | Simona Fišnarová |
| collection | DOAJ |
| description | We study the half-linear differential equation
$$
(r(t)\Phi(x'(t)))'+c(t)\Phi(x(\tau(t)))=0,\quad \Phi(x):=|x|^{p-2}x,\ p>1.
$$
We formulate new oscillation criteria for this equation by comparing it with a certain ordinary linear or half-linear differential equation. Our proofs are based on a suitable estimate for the solution of the equation studied and on the modified Riccati technique, which, in ordinary case, appeared to be an effective replacement of the well known linear transformation formula. |
| first_indexed | 2024-04-09T13:39:58Z |
| format | Article |
| id | doaj.art-eafc57a558ef4decb919541cce6947a4 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:58Z |
| publishDate | 2014-12-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-eafc57a558ef4decb919541cce6947a42023-05-09T07:53:04ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752014-12-0120146411410.14232/ejqtde.2014.1.643344Modified Riccati technique for half-linear differential equations with delaySimona Fišnarová0Robert Marik1Mendel University in Brno, Brno, Czech RepublicMendel University in Brno, Brno, Czech RepublicWe study the half-linear differential equation $$ (r(t)\Phi(x'(t)))'+c(t)\Phi(x(\tau(t)))=0,\quad \Phi(x):=|x|^{p-2}x,\ p>1. $$ We formulate new oscillation criteria for this equation by comparing it with a certain ordinary linear or half-linear differential equation. Our proofs are based on a suitable estimate for the solution of the equation studied and on the modified Riccati technique, which, in ordinary case, appeared to be an effective replacement of the well known linear transformation formula.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3344half-linear differential equationdelay equationoscillation criteriamodified riccati technique |
| spellingShingle | Simona Fišnarová Robert Marik Modified Riccati technique for half-linear differential equations with delay Electronic Journal of Qualitative Theory of Differential Equations half-linear differential equation delay equation oscillation criteria modified riccati technique |
| title | Modified Riccati technique for half-linear differential equations with delay |
| title_full | Modified Riccati technique for half-linear differential equations with delay |
| title_fullStr | Modified Riccati technique for half-linear differential equations with delay |
| title_full_unstemmed | Modified Riccati technique for half-linear differential equations with delay |
| title_short | Modified Riccati technique for half-linear differential equations with delay |
| title_sort | modified riccati technique for half linear differential equations with delay |
| topic | half-linear differential equation delay equation oscillation criteria modified riccati technique |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3344 |
| work_keys_str_mv | AT simonafisnarova modifiedriccatitechniqueforhalflineardifferentialequationswithdelay AT robertmarik modifiedriccatitechniqueforhalflineardifferentialequationswithdelay |