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 |
| Published: |
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 |
| Summary: | 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]. |
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| ISSN: | 1072-6691 |