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| Oscillatory and Asymptotic Behavior of First Order Functional Differential Equations |
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Citation： |
Ruan Jiong.Oscillatory and Asymptotic Behavior of First Order Functional Differential Equations[J].Chinese Annals of Mathematics B,1985,6(2):241~250 |
| Page view： 875
Net amount： 733 |
Authors： |
Ruan Jiong; |
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| Abstract： |
In this paper the author discusses the following first order functional differential equations:
$x'(t)+[\int_a^b {p(t,\xi )x[g(t,\xi )]d\sigma (\xi ) = 0} \] (1)$
$x'(t)+[\int_a^b {f(t,\xi )x[g(t,\xi )]d\sigma (\xi ) = 0} \] (2)$
Some sufficient conditions of oscillation and nonoscillation are obtained, and two asymptotic properties and their criteria are given. These criteria are better than those in [1, 2], and can be used to the following equations:
$x'(t)+[\sum\limits_{i = 1}^n {{p_i}(t)x[{g_i}(t)] = 0} \] (3)$
$x'(t)+[\sum\limits_{i = 1}^n {{f_i}(t)x[{g_i}(t)] = 0} \] (4)$ |
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