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Applied Mathematics and Mechanics (English Edition) ›› 1990, Vol. 11 ›› Issue (9): 881-887.

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ON THE BOUNDEDNESS AND THE STABILITY PROPERTIES OF SOLUTION OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS

俞元洪1, 陈文灯2   

  1. 1. Institute of Applied Mathematics, Academia Sinica, Beijing;
    2. Beijing Institute of Technology, Beijing
  • 收稿日期:1988-03-23 出版日期:1990-09-18 发布日期:1990-09-18

ON THE BOUNDEDNESS AND THE STABILITY PROPERTIES OF SOLUTION OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS

Yu Yuan-hong1, Cheng Wen-deng2   

  1. 1. Institute of Applied Mathematics, Academia Sinica, Beijing;
    2. Beijing Institute of Technology, Beijing
  • Received:1988-03-23 Online:1990-09-18 Published:1990-09-18

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摘要： This paper investigates equation(1)in twocases:(i)P≡0,(ii)P≠0 satisfies|P(i,x,y,z,w)<(A+|y|+|z|+|w|)q(t). whereq(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.

关键词: nonlinear differential equations of the four order, boundedness, stability

Abstract: This paper investigates equation(1)in twocases:(i)P≡0,(ii)P≠0 satisfies|P(i,x,y,z,w)<(A+|y|+|z|+|w|)q(t). whereq(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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