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# Article

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Keywords:
differential equations of fourth order; boundedness; stability; Lyapunov functions
Summary:
Sufficient conditions are established for the asymptotic stability of the zero solution of the equation (1.1) with $p\equiv 0$ and the boundedness of all solutions of the equation (1.1) with $p\ne 0$. Our result includes and improves several results in the literature ([4], [5], [8]).
References:
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[4] Hu C. Y.: The stability in the large for certain fourth order differential equations. Ann. Differential Equations 8, 4 (1992), 422–428. MR 1215987 | Zbl 0776.34040
[5] Ponzo P. J.: On the stability of certain nonlinear differential equations. IEEE Trans. Automatic Control 10 (1965), 470–472. MR 0188554
[6] Reissig R., Sansone G., Conti R.: Nonlinear Differential Equations of Higher Order. : Noordhoff, Groningen. 1974.
[7] Tunç C.: A note on the stability and boundedness results of solutions of certain fourth order differential equations. Appl. Math. Comp. 155, 3 (2004), 837–843. MR 2078694
[8] Wu X., Xiong K.: Remarks on stability results for the solutions of certain fourth-order autonomous differential equations. Internat. J. Control. 69, 2 (1998), 353–360. MR 1684744 | Zbl 0934.34039

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