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Periodicity and non‐negativity of solutions for nonlinear neutral differential equations with variable delay via fixed point theorems
Author(s) -
Mesmouli Mouataz Billah,
Ardjouni Abdelouaheb,
Djoudi Ahcene
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3733
Subject(s) - mathematics , fixed point theorem , nonlinear system , negativity effect , contraction (grammar) , contraction mapping , variable (mathematics) , fixed point , differential equation , mathematical analysis , medicine , psychology , social psychology , physics , quantum mechanics
We use a modification of Krasnoselskii's fixed point theorem introduced by Burton to show the periodicity and non‐negativity of solutions for the nonlinear neutral differential equation with variable delayx ′t = − a t h x t − τ t+ c tx ′t − τ t+ G t , x t , x t − τ t. We invert this equation to construct the sum of a compact map and a large contraction, which is suitable for applying the modification of Krasnoselskii's theorem. Copyright © 2015 John Wiley & Sons, Ltd.