Non-oscillatory behaviour of higher order functional differential equations of neutral type
In this paper, we obtain sufficient conditions so that the neutral functional differential equation $$displaylines{ ig[r(t) [y(t)-p(t)y(au (t))]'ig]^{(n-1)} + q(t) G(y(h(t))) = f(t) }$$ has a bounded and positive solution. Here $ngeq 2$; $q,au, h$ are continuous functions with $q(t)...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2007-11-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2007/163/abstr.html |
| _version_ | 1811275319006461952 |
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| author | Laxmi Narayan Padhy Prayag Prasad Mishra Niyati Misra Radhanath Rath |
| author_facet | Laxmi Narayan Padhy Prayag Prasad Mishra Niyati Misra Radhanath Rath |
| author_sort | Laxmi Narayan Padhy |
| collection | DOAJ |
| description | In this paper, we obtain sufficient conditions so that the neutral functional differential equation $$displaylines{ ig[r(t) [y(t)-p(t)y(au (t))]'ig]^{(n-1)} + q(t) G(y(h(t))) = f(t) }$$ has a bounded and positive solution. Here $ngeq 2$; $q,au, h$ are continuous functions with $q(t) geq 0$; $h(t)$ and $au(t)$ are increasing functions which are less than $t$, and approach infinity as $t o infty$. In our work, $r(t) equiv 1$ is admissible, and neither we assume that $G$ is non-decreasing, that $xG(x) > 0$ for $x eq 0$, nor that $G$ is Lipschitzian. Hence the results of this paper generalize many results in [1] and [4]-[8]. |
| first_indexed | 2024-04-12T23:35:42Z |
| format | Article |
| id | doaj.art-2fdd7c9d6ecc478ab3f5de45cee865cc |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T23:35:42Z |
| publishDate | 2007-11-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-2fdd7c9d6ecc478ab3f5de45cee865cc2022-12-22T03:12:09ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912007-11-012007163114Non-oscillatory behaviour of higher order functional differential equations of neutral typeLaxmi Narayan PadhyPrayag Prasad MishraNiyati MisraRadhanath RathIn this paper, we obtain sufficient conditions so that the neutral functional differential equation $$displaylines{ ig[r(t) [y(t)-p(t)y(au (t))]'ig]^{(n-1)} + q(t) G(y(h(t))) = f(t) }$$ has a bounded and positive solution. Here $ngeq 2$; $q,au, h$ are continuous functions with $q(t) geq 0$; $h(t)$ and $au(t)$ are increasing functions which are less than $t$, and approach infinity as $t o infty$. In our work, $r(t) equiv 1$ is admissible, and neither we assume that $G$ is non-decreasing, that $xG(x) > 0$ for $x eq 0$, nor that $G$ is Lipschitzian. Hence the results of this paper generalize many results in [1] and [4]-[8].http://ejde.math.txstate.edu/Volumes/2007/163/abstr.htmlOscillatory solutionnonoscillatory solutionasymptotic behaviour |
| spellingShingle | Laxmi Narayan Padhy Prayag Prasad Mishra Niyati Misra Radhanath Rath Non-oscillatory behaviour of higher order functional differential equations of neutral type Electronic Journal of Differential Equations Oscillatory solution nonoscillatory solution asymptotic behaviour |
| title | Non-oscillatory behaviour of higher order functional differential equations of neutral type |
| title_full | Non-oscillatory behaviour of higher order functional differential equations of neutral type |
| title_fullStr | Non-oscillatory behaviour of higher order functional differential equations of neutral type |
| title_full_unstemmed | Non-oscillatory behaviour of higher order functional differential equations of neutral type |
| title_short | Non-oscillatory behaviour of higher order functional differential equations of neutral type |
| title_sort | non oscillatory behaviour of higher order functional differential equations of neutral type |
| topic | Oscillatory solution nonoscillatory solution asymptotic behaviour |
| url | http://ejde.math.txstate.edu/Volumes/2007/163/abstr.html |
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