用内禀法求解某些四阶微分方程的有界性和稳定性成果
On the Boundedness and the Stability Results for the Solution of Certain Fourth order Differential Equations via the Intrinsic Method
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摘要: 本文首先对方程(1.1)建立了Lyapunov函数,然后在P=0的情况下,证明了平庸解x=0在大范围内的渐近稳定性,和在p≠0的情况下,研究了(1.1)式的解的有界性问题。这些结论对一些众所周知的成果有所改进。
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关键词:
- 四阶微分方程 /
- Lyapunov函数 /
- 渐近稳定性 /
- 有界性 /
- 内禀法
Abstract: In this paper, we first present constructing a Lyapunov function for (1.1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p o,and the boundedness result of the solutions of (1.1) for case p=0. These results improve sveral well-known results. -
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