On the Behavior of Solutions of a Third-Order Nonlinear Dynamic Equation on Time Scales
We study oscillatory and asymptotic properties of the third-order nonlinear dynamic equation $$ {{\left[ {{{{\left( {\frac{1}{{{r_2}(t)}}{{{\left( {{{{\left( {\frac{1}{{{r_1}(t)}}{x^{\varDelta }}(t)} \right)}}^{{{\gamma_1}}}}} \right)}}^{\varDelta }}} \right)}}^{{{\gamma_2}}}}} \right]}^{\varDelta...
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| Дата: | 2013 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2013
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2484 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We study oscillatory and asymptotic properties of the third-order nonlinear dynamic equation $$ {{\left[ {{{{\left( {\frac{1}{{{r_2}(t)}}{{{\left( {{{{\left( {\frac{1}{{{r_1}(t)}}{x^{\varDelta }}(t)} \right)}}^{{{\gamma_1}}}}} \right)}}^{\varDelta }}} \right)}}^{{{\gamma_2}}}}} \right]}^{\varDelta }}+f\left( {t,{x^{\sigma }}(t)} \right)=0,\quad t\in \mathbb{T}. $$ By using the Riccati transformation, we present new criteria for the oscillation or certain asymptotic behavior of solutions of this equation. It is supposed that the time scale T is unbounded above. |
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