Yıl 2018, Cilt 2, Sayı 4, Sayfalar 184 - 194 2018-12-24
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## 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]

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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.
Birincil Dil en Matematik Articles Yazar: Hocine Gabsi (Sorumlu Yazar) Yazar: Abdelouaheb ArdjouniÜlke: Algeria Yazar: Ahcene Djoudi
 Bibtex @araştırma makalesi { 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 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 - http://dx.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 (Aralık 2018): 184-194. http://dx.doi.org/10.31197/atnaa.401104