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Keywords:
differential equations of fourth order; boundedness; stability; Lyapunov functions
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
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[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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