| Title | ASYMPTOTIC BEHAVIOR OF OSCILLATORY SOLUTIONS OF n-TH ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT DEPENDING ON THE UNKNOWN FUNCTION |
| Publication Type | Journal Article |
| Year of Publication | 2007 |
| Authors | Markova, NT, Simeonov, PS |
| Secondary Title | Communications in Applied Analysis |
| Volume | 11 |
| Issue | 2 |
| Start Page | 235 |
| Pagination | 246 |
| Date Published | 04/2007 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 34K15 |
| Abstract | The paper deals with damped oscillations of the n-th order forced differential equation:
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| URL | http://www.acadsol.eu/en/articles/11/2/6.pdf |
| Short Title | Asymptotic Behavior of Oscillatory Solutions |
| Refereed Designation | Refereed |
| Full Text | References[1] D.D. Bainov and P.S. Simeonov, Positive solutions of a superlinear first-order differential equations with delay depending on the unknown function, Jour. of Comp. and Appl. Mathematics, 88 (1998), 95-101.
[2] D.D. Bainov, N.T. Markova, and P.S. Simeonov, Asymptotic behaviour of the nonoscillatory solutions of differential equations of second order with delay depending on the unknown function, Jour. of Comp. and Appl. Math., 91 (1998), 87-96. [3] D.D. Bainov, N.T. Markova, and P.S. Simeonov, Asymptotic and oscillatory behaviour of n-th order differential equations with deviating arguments, depending on the unknown function, Jour. Comm. Appl. Anal., 7 (2003), no. 4, 455-471. [4] D.D. Bainov, N.T. Markova, and P.S. Simeonov, Oscillation of second order differential equations with retarded argument depending on the unknown function, Jour. Comm. Appl. Anal., 7 (2003), 593-604. [5] E.F. Beckenbach and R. Bellman, Inequalities, Springer Verlag, Berlin, 1961. [6] S.R. Grace and B.S. Lalli, On oscillation and nonoscillation of general functional differential equations, J. Math. Anal. Appl., 109, (1985), no. 2, 522-533. [7] J.R. Graef, Y. Kitamura, T. Kusano, H. Onose, and P.W. Spikes, On the nonoscillation of perturbed functional differential equations, Pacific J. Math., 83 (1979), 365-373. [8] T. Kusano and H. Onose, A nonoscilation theorem for a second order sublinear retarded differential equation, Bull. Austral. Math. Soc., 15 (1976), 401-406. [9] T. Kusano and H. Onose, Asymptotic decay of oscillatory solutions of second order differential equations with forcing term, Proc. Amer. Math. Soc., 66 (1977), 251-257. [10] N.T. Markova and P.S. Simeonov, Asymptotic and oscillatory properties of the solutions of differential equations with delay depending on the unknown function, Invited lectures delivered at the VII-th Int. Colloquium on Differential Equations, August 18-23, 1996, Plovdiv, Bulgaria, vol. II (1996), 71-78. [11] N.T. Markova and P.S. Simeonov, On the asymptotic behaviour of the solutions of a class of differential equations with delay depending on the unknown function, Invited lectures delivered at the VII-th Int. Colloquium on Differential Equations, August 18-23, 1996, Plovdiv, Bulgaria, vol. I (1996), 89-100. [12] N.T. Markova and P.S. Simeonov, Oscillatory and asymptotic behaviour of the solutions of first order differential equations with delays depending on the unknown function, Invited lectures delivered at the VII-th Int. Colloquium on Differential Equations, August 18-23, 1996, Plovdiv, Bulgaria, vol. II (1996), 79-92. [13] B. Singh, A correction to “Forced oscillations in general ordinary differential equations with deviating arguments”, Hiroshima Math. J., 9 (1979), 297-302.
[14] B. Singh, Necessary and sufficient condition for eventual decay of oscillations in general functional equations with delays, Hiroshima Math. J., 10 (1980), 1-9. |
