POSITIVE PERIODIC SOLUTIONS OF SECOND-ORDER SYSTEMS WITH SINGULARITIES AND DEVIATING ARGUMENTS

TitlePOSITIVE PERIODIC SOLUTIONS OF SECOND-ORDER SYSTEMS WITH SINGULARITIES AND DEVIATING ARGUMENTS
Publication TypeJournal Article
Year of Publication2016
AuthorsBESSIOUD, KARIMA, ARDJOUNI, ABDELOUAHEB, DJOUDI, AHCENE
Secondary TitleCommunications in Applied Analysis
Volume20
Issue2
Start Page223
Pagination15
Date Published06/2016
Type of Workscientific: mathematics
ISSN1083-2564
AMS34B16, 34B18, 34B27, 34K13, 47H10
Abstract

In this paper, we use Schauder’s fixed point theorem to prove that the second-order systems with singularities and deviating arguments

$$( x ′′ (t) + a1 (t) x (t) = f1 (t, y (t − τ1 (t))) + e1 (t), $$

$$y ′′ (t) + a2 (t) y (t) = f2 (t, x (t − τ2 (t))) + e2 (t),$$

has a positive periodic solution, where ai , τi ∈ L 1 (R/TZ, R+), ei ∈ L 1 (R/TZ, R) and fi (i = 1, 2) are Carath´eodory functions and have singularities at the origin. An example is also given to illustrate our work.
URLhttp://www.acadsol.eu/en/articles/20/2/4.pdf
DOI10.12732/caa.v20i4.1
Full Text

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