Study of the Periodic or Nonnegative Periodic Solutions of Functional Differential Equations via Krasnoselskii–Burton’s Theorem
In this paper, we study the existence of periodic or nonnegative periodic solutions of the nonlinear neutral differential equation d d t [ x ( t ) - Q ( t , x ( t - τ ( t ) ) ) ] = - a ( t ) h ( x ( t - τ ( t ) ) ) + G ( t , x ( t ) , x ( t - τ ( t ) ) ) . We invert this equation to construct a sum...
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| Veröffentlicht in: | Differential equations and dynamical systems 2016-10, Vol.24 (4), p.391-406 |
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| creator | Mesmouli, Mouataz Billah Ardjouni, Abdelouaheb Djoudi, Ahcene |
| description | In this paper, we study the existence of periodic or nonnegative periodic solutions of the nonlinear neutral differential equation
d
d
t
[
x
(
t
)
-
Q
(
t
,
x
(
t
-
τ
(
t
)
)
)
]
=
-
a
(
t
)
h
(
x
(
t
-
τ
(
t
)
)
)
+
G
(
t
,
x
(
t
)
,
x
(
t
-
τ
(
t
)
)
)
.
We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the modification of Krasnoselskii’s theorem. The Caratheodory condition is used for the functions
Q
and
G
. |
| doi_str_mv | 10.1007/s12591-014-0235-5 |
| format | Article |
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d
d
t
[
x
(
t
)
-
Q
(
t
,
x
(
t
-
τ
(
t
)
)
)
]
=
-
a
(
t
)
h
(
x
(
t
-
τ
(
t
)
)
)
+
G
(
t
,
x
(
t
)
,
x
(
t
-
τ
(
t
)
)
)
.
We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the modification of Krasnoselskii’s theorem. The Caratheodory condition is used for the functions
Q
and
G
.</description><identifier>ISSN: 0971-3514</identifier><identifier>EISSN: 0974-6870</identifier><identifier>DOI: 10.1007/s12591-014-0235-5</identifier><language>eng</language><publisher>New Delhi: Springer India</publisher><subject>Computer Science ; Engineering ; Mathematics ; Mathematics and Statistics ; Nonlinear differential equations ; Original Research</subject><ispartof>Differential equations and dynamical systems, 2016-10, Vol.24 (4), p.391-406</ispartof><rights>Foundation for Scientific Research and Technological Innovation 2015</rights><rights>Copyright Springer Science & Business Media 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-bdc7dded27593b60c38231980b350f9d32d61d771d64d2388a9ab0137af7948e3</citedby><cites>FETCH-LOGICAL-c316t-bdc7dded27593b60c38231980b350f9d32d61d771d64d2388a9ab0137af7948e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12591-014-0235-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12591-014-0235-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Mesmouli, Mouataz Billah</creatorcontrib><creatorcontrib>Ardjouni, Abdelouaheb</creatorcontrib><creatorcontrib>Djoudi, Ahcene</creatorcontrib><title>Study of the Periodic or Nonnegative Periodic Solutions of Functional Differential Equations via Krasnoselskii–Burton’s Theorem</title><title>Differential equations and dynamical systems</title><addtitle>Differ Equ Dyn Syst</addtitle><description>In this paper, we study the existence of periodic or nonnegative periodic solutions of the nonlinear neutral differential equation
d
d
t
[
x
(
t
)
-
Q
(
t
,
x
(
t
-
τ
(
t
)
)
)
]
=
-
a
(
t
)
h
(
x
(
t
-
τ
(
t
)
)
)
+
G
(
t
,
x
(
t
)
,
x
(
t
-
τ
(
t
)
)
)
.
We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the modification of Krasnoselskii’s theorem. The Caratheodory condition is used for the functions
Q
and
G
.</description><subject>Computer Science</subject><subject>Engineering</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinear differential equations</subject><subject>Original Research</subject><issn>0971-3514</issn><issn>0974-6870</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1kL1OwzAUhSMEEqXwAGyRmA12nMT2CKUFRAVILbPlxE7rktqtnVTqVolHYOL1-iQkhKEL0_3ROUf3fkFwieA1gpDceBQlDAGIYgAjnIDkKOhBRmKQUgKPf3sEcILi0-DM-wWEKWEx6QWfk6qW29AWYTVX4Zty2kqdh9aFL9YYNROV3hzsJ7asK22Nbx2j2uTtIMrwXheFcspUuhmG61p0oo0W4bMT3livSv-h9X73dVe7ypr97tuH07myTi3Pg5NClF5d_NV-8D4aTgePYPz68DS4HYMco7QCmcyJlEpGJGE4S2GOaYQRozDDCSyYxJFMkSQEyTSWEaZUMJFBhIkoml-pwv3gqstdObuula_4wtauOd9zRCmkScxY3KhQp8qd9d6pgq-cXgq35QjyljXvWPOGNW9Z86TxRJ3HN1ozU-4g-V_TD_lFhYI</recordid><startdate>20161001</startdate><enddate>20161001</enddate><creator>Mesmouli, Mouataz Billah</creator><creator>Ardjouni, Abdelouaheb</creator><creator>Djoudi, Ahcene</creator><general>Springer India</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20161001</creationdate><title>Study of the Periodic or Nonnegative Periodic Solutions of Functional Differential Equations via Krasnoselskii–Burton’s Theorem</title><author>Mesmouli, Mouataz Billah ; Ardjouni, Abdelouaheb ; Djoudi, Ahcene</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-bdc7dded27593b60c38231980b350f9d32d61d771d64d2388a9ab0137af7948e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Computer Science</topic><topic>Engineering</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinear differential equations</topic><topic>Original Research</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mesmouli, Mouataz Billah</creatorcontrib><creatorcontrib>Ardjouni, Abdelouaheb</creatorcontrib><creatorcontrib>Djoudi, Ahcene</creatorcontrib><collection>CrossRef</collection><jtitle>Differential equations and dynamical systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mesmouli, Mouataz Billah</au><au>Ardjouni, Abdelouaheb</au><au>Djoudi, Ahcene</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Study of the Periodic or Nonnegative Periodic Solutions of Functional Differential Equations via Krasnoselskii–Burton’s Theorem</atitle><jtitle>Differential equations and dynamical systems</jtitle><stitle>Differ Equ Dyn Syst</stitle><date>2016-10-01</date><risdate>2016</risdate><volume>24</volume><issue>4</issue><spage>391</spage><epage>406</epage><pages>391-406</pages><issn>0971-3514</issn><eissn>0974-6870</eissn><abstract>In this paper, we study the existence of periodic or nonnegative periodic solutions of the nonlinear neutral differential equation
d
d
t
[
x
(
t
)
-
Q
(
t
,
x
(
t
-
τ
(
t
)
)
)
]
=
-
a
(
t
)
h
(
x
(
t
-
τ
(
t
)
)
)
+
G
(
t
,
x
(
t
)
,
x
(
t
-
τ
(
t
)
)
)
.
We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the modification of Krasnoselskii’s theorem. The Caratheodory condition is used for the functions
Q
and
G
.</abstract><cop>New Delhi</cop><pub>Springer India</pub><doi>10.1007/s12591-014-0235-5</doi><tpages>16</tpages></addata></record> |
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| ispartof | Differential equations and dynamical systems, 2016-10, Vol.24 (4), p.391-406 |
| issn | 0971-3514 0974-6870 |
| language | eng |
| recordid | cdi_proquest_journals_1880854994 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Computer Science Engineering Mathematics Mathematics and Statistics Nonlinear differential equations Original Research |
| title | Study of the Periodic or Nonnegative Periodic Solutions of Functional Differential Equations via Krasnoselskii–Burton’s Theorem |
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