Research Article
BibTex RIS Cite

Positive solutions of second-order neutral differential equations with distributed deviating arguments

Year 2018, Volume: 34 Issue: 1, 22 - 26, 30.04.2018

Bengü Çına M. Tamer Şenel

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. The main tool for proving our results is the Banach contraction principle. For this reason, we define a conversion and we show that it's a contraction transformation. The example at the end of the article is given to illustrate the effectiveness of our results. Our results improve and extend some existing results.

Keywords

Fixed point Second-order Distributed deviating argument

References

  • A. Yang, Z. Zhang and W. Ge, Existence of nonoscillatory solutions of second-order nonlinear neutral differential equations, Indian J. Pure Appl. Math. 39(3) (2008), 227-235.
  • T. Candan and R. S.Dahiya, Existence of nonoscillatory solutions of first and secondorder neutral differential equations with distributed deviatingarguments, J. Franklin Inst. 347 (2010) 1309-1316.
  • T. Candan, Existence of Nonoscillatory Solutions of Higher Order Neutral Differential Equations, Filomat 30:8 (2016) 2147-2153.
  • T. Candan and R. S Dahiya, Existence of nonoscillatory solutionsof higher order neutral differential equations with distributeddeviating arguments, Math. Slovaca. 63(1) (2013) 183-190.
  • T. Candan, Nonoscillatory solutions of higher order differential and delay differential equations with forcing term. Appl. Math. Lett. 39 (2015), 67-72.
  • Y. Tian, Y. Cai and T. Li, Existence of nonoscillatory solutions to second-order nonlinear neutral difference equations, J. Nonlinear Sci. Appl. 8 (2015) 884-892.
  • I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations With Applications, Clarendon Press, Oxford, (1991).
  • L. H. Erbe, Q. Kong and B. G. Zhang, Oscillation Theory for Functional Differential Equations, Marcel Dekker, Inc., New York, (1995).
  • R. P. Agarwal, S. R. Grace and D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, (2000).
  • Y. Yu, H. Wang, Nonoscillatory Solutions of Second Order Nonlinear Neutral Delay Equations, J. Math. Anal. Appl. 311(2005) 445-456.

Year 2018, Volume: 34 Issue: 1, 22 - 26, 30.04.2018

Bengü Çına M. Tamer Şenel

Abstract

References

  • A. Yang, Z. Zhang and W. Ge, Existence of nonoscillatory solutions of second-order nonlinear neutral differential equations, Indian J. Pure Appl. Math. 39(3) (2008), 227-235.
  • T. Candan and R. S.Dahiya, Existence of nonoscillatory solutions of first and secondorder neutral differential equations with distributed deviatingarguments, J. Franklin Inst. 347 (2010) 1309-1316.
  • T. Candan, Existence of Nonoscillatory Solutions of Higher Order Neutral Differential Equations, Filomat 30:8 (2016) 2147-2153.
  • T. Candan and R. S Dahiya, Existence of nonoscillatory solutionsof higher order neutral differential equations with distributeddeviating arguments, Math. Slovaca. 63(1) (2013) 183-190.
  • T. Candan, Nonoscillatory solutions of higher order differential and delay differential equations with forcing term. Appl. Math. Lett. 39 (2015), 67-72.
  • Y. Tian, Y. Cai and T. Li, Existence of nonoscillatory solutions to second-order nonlinear neutral difference equations, J. Nonlinear Sci. Appl. 8 (2015) 884-892.
  • I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations With Applications, Clarendon Press, Oxford, (1991).
  • L. H. Erbe, Q. Kong and B. G. Zhang, Oscillation Theory for Functional Differential Equations, Marcel Dekker, Inc., New York, (1995).
  • R. P. Agarwal, S. R. Grace and D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, (2000).
  • Y. Yu, H. Wang, Nonoscillatory Solutions of Second Order Nonlinear Neutral Delay Equations, J. Math. Anal. Appl. 311(2005) 445-456.
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Bengü Çına

M. Tamer Şenel

Publication Date April 30, 2018
Published in Issue Year 2018 Volume: 34 Issue: 1

Cite

APA Çına, B., & Şenel, M. T. (2018). Positive solutions of second-order neutral differential equations with distributed deviating arguments. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, 34(1), 22-26.
AMA Çına B, Şenel MT. Positive solutions of second-order neutral differential equations with distributed deviating arguments. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi. April 2018;34(1):22-26.
Chicago Çına, Bengü, and M. Tamer Şenel. “Positive Solutions of Second-Order Neutral Differential Equations With Distributed Deviating Arguments”. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi 34, no. 1 (April 2018): 22-26.
EndNote Çına B, Şenel MT (April 1, 2018) Positive solutions of second-order neutral differential equations with distributed deviating arguments. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi 34 1 22–26.
IEEE B. Çına and M. T. Şenel, “Positive solutions of second-order neutral differential equations with distributed deviating arguments”, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, vol. 34, no. 1, pp. 22–26, 2018.
ISNAD Çına, Bengü - Şenel, M. Tamer. “Positive Solutions of Second-Order Neutral Differential Equations With Distributed Deviating Arguments”. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi 34/1 (April 2018), 22-26.
JAMA Çına B, Şenel MT. Positive solutions of second-order neutral differential equations with distributed deviating arguments. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi. 2018;34:22–26.
MLA Çına, Bengü and M. Tamer Şenel. “Positive Solutions of Second-Order Neutral Differential Equations With Distributed Deviating Arguments”. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, vol. 34, no. 1, 2018, pp. 22-26.
Vancouver Çına B, Şenel MT. Positive solutions of second-order neutral differential equations with distributed deviating arguments. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi. 2018;34(1):22-6.

✯ Etik kurul izni gerektiren, tüm bilim dallarında yapılan araştırmalar için etik kurul onayı alınmış olmalı, bu onay makalede belirtilmeli ve belgelendirilmelidir.
✯ Etik kurul izni gerektiren araştırmalarda, izinle ilgili bilgilere (kurul adı, tarih ve sayı no) yöntem bölümünde, ayrıca makalenin ilk/son sayfalarından birinde; olgu sunumlarında, bilgilendirilmiş gönüllü olur/onam formunun imzalatıldığına dair bilgiye makalede yer verilmelidir.
✯ Dergi web sayfasında, makalelerde Araştırma ve Yayın Etiğine uyulduğuna dair ifadeye yer verilmelidir.
✯ Dergi web sayfasında, hakem, yazar ve editör için ayrı başlıklar altında etik kurallarla ilgili bilgi verilmelidir.
✯ Dergide ve/veya web sayfasında, ulusal ve uluslararası standartlara atıf yaparak, dergide ve/veya web sayfasında etik ilkeler ayrı başlık altında belirtilmelidir. Örneğin; dergilere gönderilen bilimsel yazılarda, ICMJE (International Committee of Medical Journal Editors) tavsiyeleri ile COPE (Committee on Publication Ethics)’un Editör ve Yazarlar için Uluslararası Standartları dikkate alınmalıdır.
✯ Kullanılan fikir ve sanat eserleri için telif hakları düzenlemelerine riayet edilmesi gerekmektedir.