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Year 2021, , 327 - 332, 30.06.2021

M. Tamer Senel , Bengü Çına

https://doi.org/10.17776/csj.826062

Abstract

References

  • [1] Yang A., Zhang Z., Ge W., Existence of nonoscillatory solutions of second-order nonlinear neutral differential equations, Indian J. Pure Appl. Math., 39 (3) (2008).
  • [2] Candan T., and Dahiya R. S., Existence of nonoscillatory solutions of first and second order neutral differential equations with distributed deviating arguments, J. Franklin Inst., 3 (47) (2010) 1309-1316.
  • [3] Candan T., Existence of Nonoscillatory Solutions of Higher Order Neutral Differential Equations, Filomat, 30 (8) (2016) 2147-2153.
  • [4] Li T., Pintus N., Viglialoro G., Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys., 70 (3) (2019) 1-18.
  • [5] Li T., Rogovchenko Yu. V., On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett., 105 (2020) 1-7.
  • [6] Candan T., Dahiya R. S., Existence of nonoscillatory solutions of higher order neutral differential equations with distributed deviating arguments, Math. Slovaca, 6 3(1) (2013) 183-190.
  • [7] Candan T., Nonoscillatory solutions of higher order differential and delay differential equations with forcing term, Appl. Math. Lett., 3 9 (2015), 67-72.
  • [8] Tian Y., Cai Y., Li T., Existence of nonoscillatory solutions to second-order nonlinear neutral difference equations, J. Nonlinear Sci. Appl., 8 (2015) 884-892.
  • [9] Györi I., Ladas G., Oscillation Theory of Delay Differential Equations With Applications, Oxford: Clarendon Press, (1991).
  • [10] Erbe L. H., Kong Q., Zang B. G., Oscillation Theory for Functional Differential Equations, New York: Marcel Dekker, Inc., (1995).
  • [11] Agarwal R. P., Grace S. R., O'Regan D., Oscillation Theory for Difference and Functional Differential Equations Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, (2000).
  • [12] Yu Y., Wang H., Nonoscillatory Solutions of Second Order Nonlinear Neutral Delay Equations, J.Math. Anal. Appl., 311(2005) 445-456.
  • [13] Li T., Han Z., Sun S., Yang D., Existence of nonoscillatory solutions to second-order neutral delay dynamic equations on time scales, Adv. Difference Equ., 2009 (2009) 562329.
  • [14] Agarval R. P., Bohner M., Li T., Zang C., A new approach in the study of oscillatory behavior of even-order neutral delay differential equations, Appl. Math. Comput., 225 (2013) 787-794.
  • [15] Džurina J., Grace S. R., Jadlovská I., Li T., Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293(5) (2020) 910-922.
  • [16] Li T., Rogovchenko Yu. V., Oscillation of second-order neutral differential equations, Math. Nachr., 88(10) (2015) 1150-1162.

Existence of nonoscillatory solutions of second-order neutral differential equations

Year 2021, , 327 - 332, 30.06.2021

M. Tamer Senel , Bengü Çına

https://doi.org/10.17776/csj.826062

Abstract

In this study we shall obtain some sufficient conditions for the existence of positive solutions of variable coefficient nonlinear second-order neutral differential equation with distributed deviating arguments. For some different cases of the range of p(t) by using Banach contraction principle we will give some sufficient conditions for the nonoscillatory solutions of second-order neutral differential equation. With this purpose we will use fixpoint theorem. At the end of the research, there is an example that meets the conditions we have given. Our results improve and extend some existing results.

Keywords

Nonoscillatory solutions Fix point Second-order

References

  • [1] Yang A., Zhang Z., Ge W., Existence of nonoscillatory solutions of second-order nonlinear neutral differential equations, Indian J. Pure Appl. Math., 39 (3) (2008).
  • [2] Candan T., and Dahiya R. S., Existence of nonoscillatory solutions of first and second order neutral differential equations with distributed deviating arguments, J. Franklin Inst., 3 (47) (2010) 1309-1316.
  • [3] Candan T., Existence of Nonoscillatory Solutions of Higher Order Neutral Differential Equations, Filomat, 30 (8) (2016) 2147-2153.
  • [4] Li T., Pintus N., Viglialoro G., Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys., 70 (3) (2019) 1-18.
  • [5] Li T., Rogovchenko Yu. V., On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett., 105 (2020) 1-7.
  • [6] Candan T., Dahiya R. S., Existence of nonoscillatory solutions of higher order neutral differential equations with distributed deviating arguments, Math. Slovaca, 6 3(1) (2013) 183-190.
  • [7] Candan T., Nonoscillatory solutions of higher order differential and delay differential equations with forcing term, Appl. Math. Lett., 3 9 (2015), 67-72.
  • [8] Tian Y., Cai Y., Li T., Existence of nonoscillatory solutions to second-order nonlinear neutral difference equations, J. Nonlinear Sci. Appl., 8 (2015) 884-892.
  • [9] Györi I., Ladas G., Oscillation Theory of Delay Differential Equations With Applications, Oxford: Clarendon Press, (1991).
  • [10] Erbe L. H., Kong Q., Zang B. G., Oscillation Theory for Functional Differential Equations, New York: Marcel Dekker, Inc., (1995).
  • [11] Agarwal R. P., Grace S. R., O'Regan D., Oscillation Theory for Difference and Functional Differential Equations Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, (2000).
  • [12] Yu Y., Wang H., Nonoscillatory Solutions of Second Order Nonlinear Neutral Delay Equations, J.Math. Anal. Appl., 311(2005) 445-456.
  • [13] Li T., Han Z., Sun S., Yang D., Existence of nonoscillatory solutions to second-order neutral delay dynamic equations on time scales, Adv. Difference Equ., 2009 (2009) 562329.
  • [14] Agarval R. P., Bohner M., Li T., Zang C., A new approach in the study of oscillatory behavior of even-order neutral delay differential equations, Appl. Math. Comput., 225 (2013) 787-794.
  • [15] Džurina J., Grace S. R., Jadlovská I., Li T., Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293(5) (2020) 910-922.
  • [16] Li T., Rogovchenko Yu. V., Oscillation of second-order neutral differential equations, Math. Nachr., 88(10) (2015) 1150-1162.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

M. Tamer Senel 0000-0003-1915-5697

Bengü Çına 0000-0003-1294-0983

Publication Date June 30, 2021
Submission Date November 14, 2020
Acceptance Date April 26, 2021
Published in Issue Year 2021

Cite

APA Senel, M. T., & Çına, B. (2021). Existence of nonoscillatory solutions of second-order neutral differential equations. Cumhuriyet Science Journal, 42(2), 327-332. https://doi.org/10.17776/csj.826062