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.
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Communicated by Fan Ta-chung
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Yuan-hong, Y., Wen-deng, C. On the boundedness and the stability properties of solution of certain fourth order differential equations. Appl Math Mech 11, 881–887 (1990). https://doi.org/10.1007/BF02014354
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DOI: https://doi.org/10.1007/BF02014354