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On the qualitative behavior of the solutions to second-order neutral delay differential equations

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Języki publikacji
EN
Abstrakty
EN
In this paper, we study the qualitative behavior of the solutions to second-order neutral delay differential equations of the form (r(t) ((x(t) + p(t)x(τ (t)))′)γ)′ + q(t)f (x(σ(t))) = 0. Our main tool is Lebesgue’s dominated convergence theorem. Examples illustrating the applicability of the results are also given.
Rocznik
Tom
Strony
43--56
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
  • Department of Electrical and Electronic Engineering Educators School of Pedagogical and Technological Education (ASPETE) 15122, Marousi, Athens, Greece
  • Department of Mathematics JIS College of Engineering, Kalyani, West Bengal - 741235, India
Bibliografia
  • [1] Agarwal R.P., Bohner M., Li T., Zhang C., Oscillation of second order differential equations with a sublinear neutral term, Carpathian J. Math., 30(2014), 1-6.
  • [2] Brands J.J.M.S., Oscillation theorems for second-order functional-differential equations, J. Math. Anal. Appl., 63(1)(1978), 54-64.
  • [3] Baculikova B., Dzurina J., Oscillation theorems for second order neutral differential equations, Comput. Math. Appl., 61(2011), 94-99.
  • [4] Baculikova B., Dzurina J., Oscillation theorems for second order nonlinear neutral differential equations, Comput. Math. Appl., 62(2011), 4472-4478.
  • [5] Baculikova B., Li T., Dzurina J., Oscillation theorems for second order neutral differential equations, Electron. J. Qual. Theory Differ. Equ., 74(2011), 1-13.
  • [6] Chatzarakis G.E., Grace S.R., Jadlovska I., Oscillation criteria for third-order delay differential equations, Adv. Difference Equ., (2017), 2017:330, 11 pages.
  • [7] Chatzarakis G.E., Dzurina I., Jadlovska I., New oscillation criteria for second-order half-linear advanced differential equations, ppl. Math. Comput., A, 347(2019), 404-416.
  • [8] Chatzarakis G.E., Jadlovska I., Improved oscillation results for second-order half-linear delay differential equations, Hacet. J. Math. Stat., 48(1)(2019), 170-179.
  • [9] Dzurina J., Oscillation theorems for second order advanced neutral differential equations, Tatra Mt. Math. Publ., 48(2011), 61-71.
  • [10] Grace S.R., Dzurina J., Jadlovska I., Li T., An improved approach for studying oscillation of second-order neutral delay differential equations, J. Inequ. Appl., (2018) 2018:193.
  • [11] Hale J., Theory of Functional Differential Equations, Applied Mathematical Sciences, 2nd ed. 3. New York - Heidelberg - Berlin: Springer-Verlag, 1977, 1.
  • [12] Karpuz B., Santra S.S., Oscillation theorems for second-order nonlinear delay differential equations of neutral type, Hacet. J. Math. Stat., DOI: 10.15672/HJMS.2017.542 (in press).
  • [13] Karpuz B., Necessary and sufficient conditions on the asymptotic behavior of second-order neutral delay dynamic equations with positive and negative coefficients, Math. Methods Appl. Sci., 37(2014), 1219-1231.
  • [14] Li T., Rogovchenko Y.V., Oscillation theorems for second order nonlinear neutral delay differential equations, Abst. Appl. Anal., 2014(2014), ID 594190, 1-5.
  • [15] Pinelas S., Santra S.S., Necessary and sufficient condition for oscillation of nonlinear neutral first-order differential equations with several delays, J. Fixed Point Theory Appl., 20(27)(2018). https://doi.org/10.1007/s11784-018-0506-9 (in press).
  • [16] Y. Qian Y., Xu R., Some new osciilation criteria for higher order quasi-linear neutral delay differential equations, Differ. Equ. Appl., 3(2011), 323-335.
  • [17] Santra S.S., Existence of positive solution and new oscillation criteria for nonlinear first order neutral delay differential equations, Differ. Equ. Appli., 8(1)(2016), 33-51.
  • [18] Santra S.S., Oscillation analysis for nonlinear neutral differential equations of second order with several delays, Mathematica, 59(82)(1-2)(2017), 111-123.
  • [19] Santra S.S., Oscillation analysis for nonlinear neutral differential equations of second order with several delays and forcing term, Mathematica, 61(84)(1)(2019), 63-78.
  • [20] Wong J.S.W., Necessary and sufficient conditions for oscillation of second order neutral differential equations, J. Math. Anal. Appl., 252(1)(2000), 342-352.
  • [21] Yang Q., Xu Z., Oscillation criteria for second order quasi-linear neutral delay differential equations on time scales, Comput. Math. Appl., 62(2011), 3682-3691.
  • [22] Ye L., Xu Z., Oscillation criteria for second order quasilinear neutral delay differential equations, Appl. Math. Comput., 207(2009), 388–396.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-73c251ff-061d-463d-9ba0-1ecac80b62d4
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