Sharp oscillation criteria for fourth order sub-half-linear and super-half-linear differential equations
This paper is concerned with the oscillatory behavior of the fourth-order nonlinear differential equation $$ \bigl(p(t)|x^{\prime\prime}|^{\alpha-1}\,x^{\prime\prime}\bigr)^{\prime\prime} +q(t)|x|^{\beta-1}x=0\,,\tag{E} $$ where $\alpha>0$, $\beta>0$ are constants and $p,q:[a,\infty)\to(0,\inf...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2008-11-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=346 |
| _version_ | 1827951438923300864 |
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| author | Jelena Manojlović J. Milosevic |
| author_facet | Jelena Manojlović J. Milosevic |
| author_sort | Jelena Manojlović |
| collection | DOAJ |
| description | This paper is concerned with the oscillatory behavior of the fourth-order nonlinear differential equation
$$
\bigl(p(t)|x^{\prime\prime}|^{\alpha-1}\,x^{\prime\prime}\bigr)^{\prime\prime}
+q(t)|x|^{\beta-1}x=0\,,\tag{E}
$$
where $\alpha>0$, $\beta>0$ are constants and $p,q:[a,\infty)\to(0,\infty)$ are continuous functions satisfying conditions
$$
\int_a^{\infty}\left( \frac{t}{p(t)}\right)^{\frac{1}{\alpha}}\,dt<\infty,
\int_a^{\infty}\frac{t}{\left(p(t)\right)^{\frac{1}{\alpha}}}\,dt<\infty .
$$
We will establish necessary and sufficient condition for oscillation of all solutions of the sub-half-linear equation (E) (for $\beta<\alpha$) as well as of the super-half-linear equation (E) (for $\beta>\alpha$). |
| first_indexed | 2024-04-09T13:41:47Z |
| format | Article |
| id | doaj.art-93583cb5a37a44838e97429e88911543 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:47Z |
| publishDate | 2008-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-93583cb5a37a44838e97429e889115432023-05-09T07:52:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752008-11-0120083211310.14232/ejqtde.2008.1.32346Sharp oscillation criteria for fourth order sub-half-linear and super-half-linear differential equationsJelena Manojlović0J. Milosevic1University of Nis, Nis, SerbiaUniversity of Nis, Nis, Serbia and MontenegroThis paper is concerned with the oscillatory behavior of the fourth-order nonlinear differential equation $$ \bigl(p(t)|x^{\prime\prime}|^{\alpha-1}\,x^{\prime\prime}\bigr)^{\prime\prime} +q(t)|x|^{\beta-1}x=0\,,\tag{E} $$ where $\alpha>0$, $\beta>0$ are constants and $p,q:[a,\infty)\to(0,\infty)$ are continuous functions satisfying conditions $$ \int_a^{\infty}\left( \frac{t}{p(t)}\right)^{\frac{1}{\alpha}}\,dt<\infty, \int_a^{\infty}\frac{t}{\left(p(t)\right)^{\frac{1}{\alpha}}}\,dt<\infty . $$ We will establish necessary and sufficient condition for oscillation of all solutions of the sub-half-linear equation (E) (for $\beta<\alpha$) as well as of the super-half-linear equation (E) (for $\beta>\alpha$).http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=346 |
| spellingShingle | Jelena Manojlović J. Milosevic Sharp oscillation criteria for fourth order sub-half-linear and super-half-linear differential equations Electronic Journal of Qualitative Theory of Differential Equations |
| title | Sharp oscillation criteria for fourth order sub-half-linear and super-half-linear differential equations |
| title_full | Sharp oscillation criteria for fourth order sub-half-linear and super-half-linear differential equations |
| title_fullStr | Sharp oscillation criteria for fourth order sub-half-linear and super-half-linear differential equations |
| title_full_unstemmed | Sharp oscillation criteria for fourth order sub-half-linear and super-half-linear differential equations |
| title_short | Sharp oscillation criteria for fourth order sub-half-linear and super-half-linear differential equations |
| title_sort | sharp oscillation criteria for fourth order sub half linear and super half linear differential equations |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=346 |
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