Oscillation Theorems Concerning Damped Nonlinear Differential Equations Of Second Order

المؤلفون

  • M. J. Saad
  • N. Kumaresan

DOI:

https://doi.org/10.37375/foej.v2i2.1545

الكلمات المفتاحية:

Damping terms, Nonlinear differential equations, Oscillatory solutions, Runge Kutta method

الملخص

 

      In this paper, some oscillation criteria for solutions of second order damped nonlinear differential equations of the form

are obtained. Our results improve and extend some existing results in the literature. Some examples are given with its numerical solutions, which are computed using Runge Kutta method of fourth order to illustrate our results.

المراجع

F. N. Ahmed and D. A. Ali, (2019), On the oscillation property for some nonlinear differential equations of second order, Journal of Pure & Applied Sciences, Vol. 18, p342-345.

F. V. Atkinson, (1955), On second order nonlinear oscillations. Pacific. J. Math. 5, p. 643-647.

B. Ayanlar and A. Tiryaki, (2000), Oscillation theorems for nonlinear second order differential equations with damping, Acta Math. Hungar. 89, p. 1-13.

X. Beqiri and E. Koci, (2014), New Oscillation and Non-oscillation Criteria For Second Order Nonlinear Differential Equations, Int. J. of Pur. and Appl. Math. 93(2), 155-163.

X. Beqiri and E. Koci, (2022), Some oscillation criteria for second order nonlinear differentail equations. Journal of Natural Sciences and Mathematics of UT, 7 (13-14). p. 151-157.

I. Bihari, (1963), An oscillation theorem concerning the half linear differential equation of the second order, Magyar Tud. Akad. Mat. Kutato Int.Kozl. 8, p. 275-280.

Chung-Fen Lee, Chen-Chin Yeh, (2007), An oscillation theorem, Applied Mathematics Letters 20, p. 238-240.

E. M. El-abbasy, Taher S. Hassan, Samir H. Saker, (2005), Oscillation of second- order non-linear differential equations with a damping term, Electronic Journal of differential equations vol.76, p.1-13.

E. M. Elabbasy1 and W. W. Elhaddad, (2007), Oscillation of second order non-linear differential equations with a damping term. Electronic Journal of Qualitative Theory of Differential Equations, No. 25, p. 1-19

W. B. Fite, (1918), Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math. Soc.19, p. 341-352.

J. R. Greaf, S. M. Rankin and P. W. Spikes, (1978), Oscillation theorems for perturbed nonlinear differential equations, J. Math. Anal. Appl. 65, p. 375-390.

I. V. Kamenev, (1978), Integral criterion for oscillation of linear differential equations of second order, Math. Zametki 23, p. 249-251.

A. G. Kartsatos, (1968), On oscillations of nonlinear equations of second order, J. Math. Anal. Appl. 24, p. 665-668.

M. Kirane and Y. V. Rogovchenko, (2000), Oscillation results for second order damped differential equations with nonmonotonous nonlinearity, J. Math. Anal. Appl. 250, p. 118-138.

J. V. Manojlovic, (2001), Integral averages and oscillation of second order nonlinear differential equations, Computers and Math. Applic. 41, p.1521-1534.

Moussadek Remili, (2010), Oscillation criteria for second order nonlinear perturbed differential equations, Electronic Journal of Qualitative Theory of Differential Equations, No.25, p. 1-11.

R. Rani and S. Kavitha, (2017), Oscillation Criteria Of Second Order Nonlinear Interval Forced Differential Equations, IJARIIE, 3(4),374-382.

M. J. Saad, N. Kumaresan and Kuru Ratnavelu, (2012), Oscillation of Second Order Nonlinear Ordinary Differential Equation with Alternating Coefficients, Commu. in Comp. and Info. Sci. 283, 367-373.

M. J. Saad, N. Kumaresan and Kuru Ratnavelu, (2013), Oscillation Theorems for Nonlinear Second Order Equations with Damping, Bull. Malays. Math. Sci. Soc.(2) 36(4), p.881-893.

M. J. Saad, N. Kumaresan and Kuru Ratnavelu, (2019), On Oscillation of Nonlinear Differential Equations of Second Order. Sirte University Scientific Journal (Applied Sciences). Vol.9 (1), p.109- 122.

M. J. Saad, N. Kumaresan and Kuru Ratnavelu, (2019), Some Oscillation Theorems for Second Order Nonlinear and Nonhomogeneous Differential Equations with alternating coefficients. Journal of Pure & Applied Sciences. Vol.18 No. (1), p. 65-73.

M. J. Saad, N. Kumaresan and Kuru Ratnavelu, (2022), Oscillation Criterion for Second Order Nonlinear Differential Equations. Journal of Educational. (20), p.302-314.

C. C. Travis, (1972), Oscillation theorems for second order differential equation with functional arguments, Proc. Math. Soc. 31,p. 199-202.

P. Waltman, (1965), An oscillation criterion for a nonlinear second order equation, J. Math. Anal. Appl. 10, p. 439-441.

A. Wintner, (1949), A criterion of oscillatory stability, Quart. Appl. Math. 7, p. 115-117.

J. S. W. Wong, (1973), A second order nonlinear oscillation theorems, Proc. Amer. Math. Soc. 40, p. 487-491.

التنزيلات

منشور

2023-07-02

كيفية الاقتباس

Saad, M. J., & Kumaresan, N. (2023). Oscillation Theorems Concerning Damped Nonlinear Differential Equations Of Second Order. المجلة العلمية لكلية التربية, 2(2), 32–15. https://doi.org/10.37375/foej.v2i2.1545

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القسم

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