On the Boundedness and the Stability Properties of Solution of Certain Fourth Order Differential Equations

Yu Yuan-hong; Cheng Wen-deng

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Article Navigation > Applied Mathematics and Mechanics > 1990 > 11(9): 827-832

Yu Yuan-hong, Cheng Wen-deng. On the Boundedness and the Stability Properties of Solution of Certain Fourth Order Differential Equations[J]. Applied Mathematics and Mechanics, 1990, 11(9): 827-832.

Citation:

Yu Yuan-hong, Cheng Wen-deng. On the Boundedness and the Stability Properties of Solution of Certain Fourth Order Differential Equations[J]. Applied Mathematics and Mechanics, 1990, 11(9): 827-832.

Citation:

Yu Yuan-hong, Cheng Wen-deng. On the Boundedness and the Stability Properties of Solution of Certain Fourth Order Differential Equations[J]. Applied Mathematics and Mechanics, 1990, 11(9): 827-832.

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On the Boundedness and the Stability Properties of Solution of Certain Fourth Order Differential Equations

Yu Yuan-hong¹,
Cheng Wen-deng²

1.
Institute of Applied Mathematics, Academic Sinica, Beijing;
2.
Beijing Institute of Technology, Beijing

Received Date: 1988-03-23
Publish Date: 1990-09-15

Abstract

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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References(5)

References

[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).