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| Asymptotic Behavior of Solutions to Second-Order Nonlinear Differential Equations |
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Citation： |
Liang Zhongchao,Chen Shaozhu.Asymptotic Behavior of Solutions to Second-Order Nonlinear Differential Equations[J].Chinese Annals of Mathematics B,1985,6(4):481~490 |
| Page view： 728
Net amount： 1170 |
Authors： |
Liang Zhongchao; Chen Shaozhu |
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| Abstract： |
In this paper the authors study the oscillation and the asymptotic behavior of solutiosn to the second-order nonlinear differential equations
$[\ddot x]\pmX(t,x,[\dot x])=0$(X_{\pm})
and give necessary and sufficient conditions for Equation (X_+) to have a bounded nonoscillatory solution or to be oscillatory. There are four classes of solutions to Equation (X_) with different asymptotic behavior. For each class of solution, the necessary or sufficient condition of the existence is obtained. |
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