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AUTHOR(S):

Gevorg Grigorian

 

TITLE

Oscillatory and nonoscillatory criteria for solutions of second order linear differential functional equations

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ABSTRACT

Riccati equation method is used to establish oscillatory and non oscillatory criteria for solutions of second order linear differential functional equations. On examples the obtained result is compared with some criteria of work of L. Berezansky and E. Braverman

KEYWORDS

Riccati equations, oscillation, nonoscillation, suboscillation.

REFERENCES

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[2] J. Durina. Oscillation theorems for second order advanced neutral differential equations. Tatra Mt. Math. Pub. 48, pp. 61 - 71. 2011. 

[3] 3. Ch. Zeng, R. P. Agraval, M. Bohner and T. Li. Properties of higher - order half - linear functional - differential equations with noncanonical operators. Advances in Difference equations, 2013, 54, pp. 1 - 10, 2013. 

[4] J. Ohrishka. Oscillation of second - order linear delay differential equations. Cent. Eur. J. Math. N ◦ 6 (3), pp. 439 - 452, 2008. 

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[9] G. P. Peliuqh, D. V. Belskij, On asymptotic properties of the solutions of the differential- - functional equations. Nelinejni kolyvanija, vol 10, N◦ 1, 2007, pp. 144 - 160, 

[10] J. Ohririska, Oscillation of second - order linear delay differential equations. Cent. Eur. J. Math., 6(3) 2008, pp. 439 - 452. 

[11] L. Berezansky, E. Braverman and H. Acka, Oscillation of linear delay integro - differential equations. Dinamic systems and Applications, v. 8 1999, pp. 219 - 235. 

[12] G. A. Grigorian, On two comparison tests for second-order linear ordinary differential equations (Russian) Differ. Uravn. 47 (2011), no. 9, 1225 - 1240; translation in Differ. Equ. 47 (2011), no. 9 1237 - 1252, 34C10. 

[13] G. A. Grigorian, On some properties of solutions of the Riccati equation. Izvestiya NAS of Armenia, vol. 42, N◦ 4, 2007, pp. 11 - 26 

[14] G. A. Grigorian, Two comparison criteria for the scalar Riccai equations and some their applications. Izv. vuzov, Matematica, N◦ 11, 2012, pp. 20 - 35.

Cite this paper

Gevorg Grigorian. (2016) Oscillatory and nonoscillatory criteria for solutions of second order linear differential functional equations. International Journal of Mathematical and Computational Methods, 1, 69-74

 

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