一类四阶微分方程解的有界性和稳定性
On the Boundedness and the Stability Properties of Solution of Certain Fourth Order Differential Equations
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摘要: 本文分两种情况研究方程(1):(i)P≡0,(ii)P(≠0)满足|P(t,x,y,z,ω)|≤(A+|y|+|z|+|ω|)q(t),这里,q(t)是t的非负函数.对于第一种情况研究了零解的全局渐近稳定性,对于第二种情况得到了方程(1)的有界性结果.这些结果改进并包含了一些已知的结果.Abstract: This paper investigates equation(1)in two cases:(i)P≡0,(ii)P≠0 satisfies|P(i,x,y,z,w)<(A+|y|+|z|+|w|)q(t). where q(t) is a nonnegative function of t. For case(i)the asymptotic stability in the large of the trivial solution x=0 is investigated and for case(ii) the boundedness result is obtained for solutions of equation(1). These results improve and include several well-known results.
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[1] Reissig,R.,G.Sansone,and R.Conti,Nonlinear Differential Equations of Higher Order,Noodhoff Lenden(1974). [2] 王慕秋、王联,《运动稳定性理论与应用》,科学出版社(1981), [3] 沈家骥、金均,四阶方程Ляпунов函数的作法与应用,上海师院学报,2(1982). [4] 卢亭鹤、金均,一类四阶方程Ляпунов函数的作图法,上海师院学报,3 (1983). [5] 关于非线性四阶方程解的稳定性,北京工业大学学报,2 (1984).
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