Year 2018, Volume 2, Issue 4, Pages 184 - 194 2018-12-24

Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays

Hocine Gabsi [1] , Abdelouaheb Ardjouni [2] , Ahcene Djoudi [3]

64 116

We consider two types of second-order neutral functional differential equations with infinite distributed delays and offer existence criteria for periodic solutions. During the process we invert the integro-differential equations into equivalent integral equations and derive suitable fixed point mappings. We show that these mappings fit into the framework of Schauder's fixed point theorem so that periodic solutions are readily obtained.
Second order, Nonlinear neutral differential equations, Periodic solutions, Fixed point theorem, Distributed delays.
  • 1) A. Ardjouni, A. Rezaiguia and A. Djoudi, Existence of positive periodic solutions for two types of second-order nonlinear neutral differential equations with infinite distributed delay, J. Appl. Math. Comput. (2015) 47:291--314.
  • A. Ardjouni, A. Djoudi, Existence of positive periodic solutions for two types of second order nonlinear neutral differential equations with variable delay, Proyecciones J. Math. 32 (4) (2013) 377--391.
  • A. Ardjouni, A. Djoudi, Existence of periodic solutions in totally nonlinear neutral dynamic equations with variable delay on a time scale, Math. Eng. Sci. Aerosp. MESA 4 (3) (2013) 305--318.
  • A. Ardjouni, A. Djoudi, Existence of positive periodic solutions for two kinds of nonlinear neutral differential equations with variable delay, Dyn. Continuous Discrete Impulsive Syst. Ser. A Math. Anal. 20 (2013) 357--366.
Primary Language en
Subjects Mathematics
Journal Section Articles
Authors

Author: Hocine Gabsi (Primary Author)

Author: Abdelouaheb Ardjouni
Country: Algeria


Author: Ahcene Djoudi

Dates

Publication Date: December 24, 2018

Bibtex @research article { atnaa401104, journal = {Advances in the Theory of Nonlinear Analysis and its Application}, issn = {}, eissn = {2587-2648}, address = {Erdal KARAPINAR}, year = {2018}, volume = {2}, pages = {184 - 194}, doi = {10.31197/atnaa.401104}, title = {Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays}, key = {cite}, author = {Gabsi, Hocine and Ardjouni, Abdelouaheb and Djoudi, Ahcene} }
APA Gabsi, H , Ardjouni, A , Djoudi, A . (2018). Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays. Advances in the Theory of Nonlinear Analysis and its Application, 2 (4), 184-194. DOI: 10.31197/atnaa.401104
MLA Gabsi, H , Ardjouni, A , Djoudi, A . "Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays". Advances in the Theory of Nonlinear Analysis and its Application 2 (2018): 184-194 <http://dergipark.org.tr/atnaa/issue/39947/401104>
Chicago Gabsi, H , Ardjouni, A , Djoudi, A . "Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays". Advances in the Theory of Nonlinear Analysis and its Application 2 (2018): 184-194
RIS TY - JOUR T1 - Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays AU - Hocine Gabsi , Abdelouaheb Ardjouni , Ahcene Djoudi Y1 - 2018 PY - 2018 N1 - doi: 10.31197/atnaa.401104 DO - 10.31197/atnaa.401104 T2 - Advances in the Theory of Nonlinear Analysis and its Application JF - Journal JO - JOR SP - 184 EP - 194 VL - 2 IS - 4 SN - -2587-2648 M3 - doi: 10.31197/atnaa.401104 UR - https://doi.org/10.31197/atnaa.401104 Y2 - 2018 ER -
EndNote %0 Advances in the Theory of Nonlinear Analysis and its Application Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays %A Hocine Gabsi , Abdelouaheb Ardjouni , Ahcene Djoudi %T Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays %D 2018 %J Advances in the Theory of Nonlinear Analysis and its Application %P -2587-2648 %V 2 %N 4 %R doi: 10.31197/atnaa.401104 %U 10.31197/atnaa.401104
ISNAD Gabsi, Hocine , Ardjouni, Abdelouaheb , Djoudi, Ahcene . "Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays". Advances in the Theory of Nonlinear Analysis and its Application 2 / 4 (December 2018): 184-194. https://doi.org/10.31197/atnaa.401104
AMA Gabsi H , Ardjouni A , Djoudi A . Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays. ATNAA. 2018; 2(4): 184-194.
Vancouver Gabsi H , Ardjouni A , Djoudi A . Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delays. Advances in the Theory of Nonlinear Analysis and its Application. 2018; 2(4): 194-184.