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Applied Mathematics and Mechanics

, Volume 11, Issue 9, pp 881–887 | Cite as

On the boundedness and the stability properties of solution of certain fourth order differential equations

  • Yu Yuan-hong
  • Cheng Wen-deng
Article
  • 21 Downloads

Abstract

This paper investigates equation (1) in two cases: (i)P≡0, (ii)P(≠0) satisfies ¦P (t,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.

Key words

nonlinear differential equations of the four order boundedness stability 

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References

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    Reissig, R., G. Sansone, and R. Conti,Nonlinear Differential Equations of Higher Order, Noodhoff Lenden (1974).Google Scholar
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    Qin Yuan-xun, Wang Mu-qiu and Wang Lian,Theory and Application of Stability of Motion, Academic Press, Beijing (1981). (in Chinese)Google Scholar
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    Lu Ting-he, Shen Jia-qi and Jin Jun, Construction and application Lyapunov function for fourth order equations,J. Shanghai Normal Univ.,2 (1982). (in Chinese)Google Scholar
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    Liang Zai-zhong, On the stability of solutions of nonlinear fourth order equations,J. Beijing Univ. Tech.,2 (1984). (in Chinese)Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1990

Authors and Affiliations

  • Yu Yuan-hong
    • 1
  • Cheng Wen-deng
    • 2
  1. 1.Institute of Applied MathematicsAcademia SinicaBeijing
  2. 2.Beijing Institute of TechnologyBeijing

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