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Yıl 2020, Cilt: 4 Sayı: 4, 385 - 393, 30.12.2020
https://doi.org/10.31197/atnaa.751034

Öz

Kaynakça

  • [1] R.P. Agarwal, L. Berzansky, E. Braverman and A. Domoshnitsky, Nonoscillation theory of functional di?erential equations with applications, Springer, 2012.
  • [2] B. Baculikova, T. Li and J. Dzurina, Oscillation theorems for second order neutral di?erential equations, Electron. J. Quali. Theo. dif. equa., (74): (2011), 1-13.
  • [3] B. Baculikova and J. Dzurina, Oscillation theorems for second order neutral diferential equations, Comput. Math. Appl., 61 (2011), 94-99.
  • [4] B. Baculikova and J. Dzurina, Oscillation theorems for second-order nonlinear neutral diferential equations, Comput. Math. Appl., 62 (2011), 4472-4478.
  • [5] C. Cesarano, O. Bazighifan, Qualitative behavior of solutions of second order diferential equations, Symmetry, 11 (2019), 1-8. [6] O. Bazighifan, C. Cesarano, Some New Oscillation Criteria for Second-Order Neutral Diferential Equations with Delayed Arguments, Mathematics, 7 (2019), 1-8.
  • [7] O. Bazighifan, M. Ruggieri, S.S. Santra, A. Scapellato, Qualitative Properties of Solutions of Second-Order Neutral Dif- ferential Equations, Symmetry, 12(9), (2020), 1520; DOI:10.3390/sym12091520.
  • [8] O. Bazighifan, Kamenev and Philos-types oscillation criteria for fourth-order neutral diferential equations, Adv. Diference Equ., 201 (2020), 1-12.
  • [9] O. Moaaz, E.M. Elabbasy, B. Qaraad, An improved approach for studying oscillation of generalized Emden Fowler neutral di?erential equation, J. Inequal. Appl. 2020, 2020, 69.
  • [10] O. Moaaz, New criteria for oscillation of nonlinear neutral di?erential equations, Adv. Difer. Equ. 2019, 2019, 484.
  • [11] J.J.M.S. Brands, Oscillation theorems for second-order functional-di?erential equations, J. Math. Anal. Appl. 63(1): (1978), 54-64.
  • [12] G.E. Chatzarakis, J. Dzurina and I. Jadlovska, New oscillation criteria for second-order half-linear advanced diferential equations, Appl. Math. Comput., 347 (2019), 404-416.
  • [13] G.E. Chatzarakis and I. Jadlovska, Improved oscillation results for second-order half-linear delay di?erential equations, Hacet. J. Math. Stat., 48(1): (2019), 170-179.
  • [14] G.E. Chatzarakis, J. Dzurina and I. Jadlovska, A remark on oscillatory results for neutral diferential equations, Appl. Math. Lett., 90 (2019), 124-130.
  • [15] J. Dzurina, Oscillation theorems for second order advanced neutral diferential equations, Tatra Mt. Math. Publ., DOI: 10.2478/v10127-011-0006-4, 48 (2011), 61-71.
  • [16] S. Fisnarova and R. Marik, Oscillation of neutral second order half-linear diferential equations without commutativity in delays, Math. Slovaca, 67 No. 3 (2017), 701-718.
  • [17] I. Gyori and G. Ladas, Oscillation Theory of Delay Di?erential Equations with Applications, Clarendon, Oxford, 1991.
  • [18] M. Hasanbulli and Y.V. Rogovchenko, Oscillation criteria for second order nonlinear neutral diferential equations, Appl. Math. Comput., 215 (2010), 4392-4399.
  • [19] B. Karpuz and S.S. Santra, Oscillation theorems for second-order nonlinear delay diferential equations of neutral type, Hacet J. Math. Stat., Doi: 10.15672/HJMS.2017.542 (in press)
  • [20] B. Karpuz and S. .S Santra; New criteria for the oscillation and asymptotic behavior of second-order neutral diferential equations with several delays, Turk J Math., (2020) 44: 1990 ?2003. doi:10.3906/mat-2006-103
  • [21] G.S. Ladde, V. Lakshmikantham and B.G. Zhang, Oscillation Theory of Di?erential Equations with Deviating Arguments, Marcel Dekker, New York and Basel, 1987.
  • [22] Q. Li, R. Wang, F. Chen and T. Li, Oscillation of second-order nonlinear delay diferential equations with nonpositive neutral coeficients, Adv. Dif. Equ. (2015) 2015:35. DOI 10.1186/s13662-015-0377-y.
  • [23] Y. Liu, J. Zhanga and J. Yan, Existence of oscillatory solutions of second order delay diferential equations, J. Comput. Appl. Math., 277 (2015), 17-22.
  • [24] S. Pinelas, S.S. Santra, Necessary and su?cient condition for oscillation of nonlinear neutral first-order diferential equations with several delays, J. Fixed Point Theory Appl., 20(27): (2018), 1-13.
  • [25] S. Pinelas and S.S. Santra, Necessary and suficient conditions for oscillation of nonlinear first order forced diferential equations with several delays of neutral type, Analysis, 39(3): (2019), 97-105.
  • [26] S.S. Santra, Oscillation analysis for nonlinear neutral diferential equations of second order with several delays, Mathematica, 59(82)(1-2): (2017), 111-123.
  • [27] S.S. Santra, Oscillation analysis for nonlinear neutral diferential equations of second order with several delays and forcing term, Mathematica, 61(84)(1): (2019), 63-78.
  • [28] S.S. Santra, Necessary and suficient condition for the solutions of first-order neutral diferential equations to be oscillatory or tend to zero, KYUNGPOOK Math. J., 59 (2019), 73-82.
  • [29] S.S. Santra, Necessary and suficient condition for oscillatory and asymptotic behaviour of second-order functional difer- ential equations, Krag. J. Math., 44(3): (2020), 459-473.
  • [30] S.S. Santra, O. Bazighifan, H. Ahmad and Yu-Ming Chu, Second-order diferential equation: oscillation the- orems and applications, Mathematical Problems in Engineering, Volume 2020, Article ID 8820066, 6 pages. https://doi.org/10.1155/2020/8820066.
  • [31] S.S. Santra, I. Dassios, and T. Ghosh, On the asymptotic behavior of a class of second-order non-linear neutral diferential equations with multiple delays, Axioms 2020, 9, 134; doi:10.3390/axioms9040134.
  • [32] S.S. Santra, O. Bazighifan, H. Ahmad and Shao-Wen Yao, Second-order diferential equation with multi- ple delays: oscillation theorems and applications, Complexity, Volume 2020, Article ID 8853745, 6 pages. https://doi.org/10.1155/2020/8853745
  • [33] S.S. Santra, T. Ghosh and O. Baghifan, Explicit criteria for the oscillation of second-order diferential equations with several sub-linear neutral coeficients, Advances in Diference Equations (2020) 2020:643 https://doi.org/10.1186/s13662- 020-03101-1
  • [34] J.S.W. Wong, Necessary and suficient conditions for oscillation of second order neutral diferential equations, J. Math. Anal. Appl., 252(1): (2000), 342-352.

Second-order half-linear delay differential equations: Oscillation tests

Yıl 2020, Cilt: 4 Sayı: 4, 385 - 393, 30.12.2020
https://doi.org/10.31197/atnaa.751034

Öz

In this work, we obtain necessary and sufficient conditions
for the oscillation of all solutions of second-order half-linear delay differential
equation of the form $
\bigl(r(y^{\prime})^\gamma\bigr)^{\prime}(t)+ q(t)y^\alpha(\tau(t))=0\,.$
We study this equation under the assumption $\int^{\infty}\big(r(\eta)\big)^{-1/\gamma} d\eta=\infty$ and consider two cases when $\gamma > \alpha$ and $\gamma < \alpha$. We provide examples, illustrating the results and state an open problem.

Kaynakça

  • [1] R.P. Agarwal, L. Berzansky, E. Braverman and A. Domoshnitsky, Nonoscillation theory of functional di?erential equations with applications, Springer, 2012.
  • [2] B. Baculikova, T. Li and J. Dzurina, Oscillation theorems for second order neutral di?erential equations, Electron. J. Quali. Theo. dif. equa., (74): (2011), 1-13.
  • [3] B. Baculikova and J. Dzurina, Oscillation theorems for second order neutral diferential equations, Comput. Math. Appl., 61 (2011), 94-99.
  • [4] B. Baculikova and J. Dzurina, Oscillation theorems for second-order nonlinear neutral diferential equations, Comput. Math. Appl., 62 (2011), 4472-4478.
  • [5] C. Cesarano, O. Bazighifan, Qualitative behavior of solutions of second order diferential equations, Symmetry, 11 (2019), 1-8. [6] O. Bazighifan, C. Cesarano, Some New Oscillation Criteria for Second-Order Neutral Diferential Equations with Delayed Arguments, Mathematics, 7 (2019), 1-8.
  • [7] O. Bazighifan, M. Ruggieri, S.S. Santra, A. Scapellato, Qualitative Properties of Solutions of Second-Order Neutral Dif- ferential Equations, Symmetry, 12(9), (2020), 1520; DOI:10.3390/sym12091520.
  • [8] O. Bazighifan, Kamenev and Philos-types oscillation criteria for fourth-order neutral diferential equations, Adv. Diference Equ., 201 (2020), 1-12.
  • [9] O. Moaaz, E.M. Elabbasy, B. Qaraad, An improved approach for studying oscillation of generalized Emden Fowler neutral di?erential equation, J. Inequal. Appl. 2020, 2020, 69.
  • [10] O. Moaaz, New criteria for oscillation of nonlinear neutral di?erential equations, Adv. Difer. Equ. 2019, 2019, 484.
  • [11] J.J.M.S. Brands, Oscillation theorems for second-order functional-di?erential equations, J. Math. Anal. Appl. 63(1): (1978), 54-64.
  • [12] G.E. Chatzarakis, J. Dzurina and I. Jadlovska, New oscillation criteria for second-order half-linear advanced diferential equations, Appl. Math. Comput., 347 (2019), 404-416.
  • [13] G.E. Chatzarakis and I. Jadlovska, Improved oscillation results for second-order half-linear delay di?erential equations, Hacet. J. Math. Stat., 48(1): (2019), 170-179.
  • [14] G.E. Chatzarakis, J. Dzurina and I. Jadlovska, A remark on oscillatory results for neutral diferential equations, Appl. Math. Lett., 90 (2019), 124-130.
  • [15] J. Dzurina, Oscillation theorems for second order advanced neutral diferential equations, Tatra Mt. Math. Publ., DOI: 10.2478/v10127-011-0006-4, 48 (2011), 61-71.
  • [16] S. Fisnarova and R. Marik, Oscillation of neutral second order half-linear diferential equations without commutativity in delays, Math. Slovaca, 67 No. 3 (2017), 701-718.
  • [17] I. Gyori and G. Ladas, Oscillation Theory of Delay Di?erential Equations with Applications, Clarendon, Oxford, 1991.
  • [18] M. Hasanbulli and Y.V. Rogovchenko, Oscillation criteria for second order nonlinear neutral diferential equations, Appl. Math. Comput., 215 (2010), 4392-4399.
  • [19] B. Karpuz and S.S. Santra, Oscillation theorems for second-order nonlinear delay diferential equations of neutral type, Hacet J. Math. Stat., Doi: 10.15672/HJMS.2017.542 (in press)
  • [20] B. Karpuz and S. .S Santra; New criteria for the oscillation and asymptotic behavior of second-order neutral diferential equations with several delays, Turk J Math., (2020) 44: 1990 ?2003. doi:10.3906/mat-2006-103
  • [21] G.S. Ladde, V. Lakshmikantham and B.G. Zhang, Oscillation Theory of Di?erential Equations with Deviating Arguments, Marcel Dekker, New York and Basel, 1987.
  • [22] Q. Li, R. Wang, F. Chen and T. Li, Oscillation of second-order nonlinear delay diferential equations with nonpositive neutral coeficients, Adv. Dif. Equ. (2015) 2015:35. DOI 10.1186/s13662-015-0377-y.
  • [23] Y. Liu, J. Zhanga and J. Yan, Existence of oscillatory solutions of second order delay diferential equations, J. Comput. Appl. Math., 277 (2015), 17-22.
  • [24] S. Pinelas, S.S. Santra, Necessary and su?cient condition for oscillation of nonlinear neutral first-order diferential equations with several delays, J. Fixed Point Theory Appl., 20(27): (2018), 1-13.
  • [25] S. Pinelas and S.S. Santra, Necessary and suficient conditions for oscillation of nonlinear first order forced diferential equations with several delays of neutral type, Analysis, 39(3): (2019), 97-105.
  • [26] S.S. Santra, Oscillation analysis for nonlinear neutral diferential equations of second order with several delays, Mathematica, 59(82)(1-2): (2017), 111-123.
  • [27] S.S. Santra, Oscillation analysis for nonlinear neutral diferential equations of second order with several delays and forcing term, Mathematica, 61(84)(1): (2019), 63-78.
  • [28] S.S. Santra, Necessary and suficient condition for the solutions of first-order neutral diferential equations to be oscillatory or tend to zero, KYUNGPOOK Math. J., 59 (2019), 73-82.
  • [29] S.S. Santra, Necessary and suficient condition for oscillatory and asymptotic behaviour of second-order functional difer- ential equations, Krag. J. Math., 44(3): (2020), 459-473.
  • [30] S.S. Santra, O. Bazighifan, H. Ahmad and Yu-Ming Chu, Second-order diferential equation: oscillation the- orems and applications, Mathematical Problems in Engineering, Volume 2020, Article ID 8820066, 6 pages. https://doi.org/10.1155/2020/8820066.
  • [31] S.S. Santra, I. Dassios, and T. Ghosh, On the asymptotic behavior of a class of second-order non-linear neutral diferential equations with multiple delays, Axioms 2020, 9, 134; doi:10.3390/axioms9040134.
  • [32] S.S. Santra, O. Bazighifan, H. Ahmad and Shao-Wen Yao, Second-order diferential equation with multi- ple delays: oscillation theorems and applications, Complexity, Volume 2020, Article ID 8853745, 6 pages. https://doi.org/10.1155/2020/8853745
  • [33] S.S. Santra, T. Ghosh and O. Baghifan, Explicit criteria for the oscillation of second-order diferential equations with several sub-linear neutral coeficients, Advances in Diference Equations (2020) 2020:643 https://doi.org/10.1186/s13662- 020-03101-1
  • [34] J.S.W. Wong, Necessary and suficient conditions for oscillation of second order neutral diferential equations, J. Math. Anal. Appl., 252(1): (2000), 342-352.
Toplam 33 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

O. Bazighifan 0000-0002-7251-9608

Shyam Sundar Santra

Yayımlanma Tarihi 30 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 4 Sayı: 4

Kaynak Göster