Stability criteria for certain third-order delay differential equations
In this paper, we study the asymptotic stability of the zero solution of third-order linear delay differential equations of the form y ‴ ( t ) = p 1 y ″ ( t ) + p 2 y ″ ( t - τ ) + q 1 y ′ ( t ) + q 2 y ′ ( t - τ ) + v 1 y ( t ) + v 2 y ( t - τ ) , where p 1 , p 2 , q 1 , q 2 , v 1 and v 2 are certa...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2006-04, Vol.188 (2), p.319-335 |
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| container_title | Journal of computational and applied mathematics |
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| creator | Cahlon, Baruch Schmidt, Darrell |
| description | In this paper, we study the asymptotic stability of the zero solution of third-order linear delay differential equations of the form
y
‴
(
t
)
=
p
1
y
″
(
t
)
+
p
2
y
″
(
t
-
τ
)
+
q
1
y
′
(
t
)
+
q
2
y
′
(
t
-
τ
)
+
v
1
y
(
t
)
+
v
2
y
(
t
-
τ
)
,
where
p
1
,
p
2
,
q
1
,
q
2
,
v
1
and
v
2
are certain constants. Here
τ
>
0
is a constant delay. In proving our results we make use of Pontryagin's theory for quasi-polynomials. |
| doi_str_mv | 10.1016/j.cam.2005.04.034 |
| format | Article |
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y
‴
(
t
)
=
p
1
y
″
(
t
)
+
p
2
y
″
(
t
-
τ
)
+
q
1
y
′
(
t
)
+
q
2
y
′
(
t
-
τ
)
+
v
1
y
(
t
)
+
v
2
y
(
t
-
τ
)
,
where
p
1
,
p
2
,
q
1
,
q
2
,
v
1
and
v
2
are certain constants. Here
τ
>
0
is a constant delay. In proving our results we make use of Pontryagin's theory for quasi-polynomials.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/j.cam.2005.04.034</identifier><identifier>CODEN: JCAMDI</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Asymptotic stability ; Characteristic functions ; Delay ; Exact sciences and technology ; Integral equations ; Mathematical analysis ; Mathematics ; Ordinary differential equations ; Sciences and techniques of general use ; Stability criteria ; Stability regions ; Sufficient conditions</subject><ispartof>Journal of computational and applied mathematics, 2006-04, Vol.188 (2), p.319-335</ispartof><rights>2005 Elsevier B.V.</rights><rights>2006 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c401t-d4a3b9832a59e5f7795c15476a2a40c33ac9935369e51b0ddee9fa0b10600f5c3</citedby><cites>FETCH-LOGICAL-c401t-d4a3b9832a59e5f7795c15476a2a40c33ac9935369e51b0ddee9fa0b10600f5c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S037704270500258X$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65534</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=17516281$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Cahlon, Baruch</creatorcontrib><creatorcontrib>Schmidt, Darrell</creatorcontrib><title>Stability criteria for certain third-order delay differential equations</title><title>Journal of computational and applied mathematics</title><description>In this paper, we study the asymptotic stability of the zero solution of third-order linear delay differential equations of the form
y
‴
(
t
)
=
p
1
y
″
(
t
)
+
p
2
y
″
(
t
-
τ
)
+
q
1
y
′
(
t
)
+
q
2
y
′
(
t
-
τ
)
+
v
1
y
(
t
)
+
v
2
y
(
t
-
τ
)
,
where
p
1
,
p
2
,
q
1
,
q
2
,
v
1
and
v
2
are certain constants. Here
τ
>
0
is a constant delay. In proving our results we make use of Pontryagin's theory for quasi-polynomials.</description><subject>Asymptotic stability</subject><subject>Characteristic functions</subject><subject>Delay</subject><subject>Exact sciences and technology</subject><subject>Integral equations</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Ordinary differential equations</subject><subject>Sciences and techniques of general use</subject><subject>Stability criteria</subject><subject>Stability regions</subject><subject>Sufficient conditions</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAQhi0EEqXwA9iywJZwju04ERNCfElIDMBsXe2zcJUmre0i9d-TqkhsTDfc876nexi75FBx4M3NsrK4qmoAVYGsQMgjNuOt7kqudXvMZiC0LkHW-pSdpbQEgKbjcsae3jMuQh_yrrAxZIoBCz_GwlLMGIYif4XoyjE6ioWjHneFC95TpCEH7AvabDGHcUjn7MRjn-jid87Z5-PDx_1z-fr29HJ_91paCTyXTqJYdK2oUXWkvNadslxJ3WCNEqwQaLtOKNFMW74A54g6j7Dg0AB4ZcWcXR9613HcbCllswrJUt_jQOM2mbrVSuipYc74AbRxTCmSN-sYVhh3hoPZKzNLMykze2UGpJmUTZmr33JMFnsfcbAh_QW14k3d8om7PXA0ffodKJpkAw2WXIhks3Fj-OfKD7xJgSY</recordid><startdate>20060415</startdate><enddate>20060415</enddate><creator>Cahlon, Baruch</creator><creator>Schmidt, Darrell</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20060415</creationdate><title>Stability criteria for certain third-order delay differential equations</title><author>Cahlon, Baruch ; Schmidt, Darrell</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c401t-d4a3b9832a59e5f7795c15476a2a40c33ac9935369e51b0ddee9fa0b10600f5c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Asymptotic stability</topic><topic>Characteristic functions</topic><topic>Delay</topic><topic>Exact sciences and technology</topic><topic>Integral equations</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Ordinary differential equations</topic><topic>Sciences and techniques of general use</topic><topic>Stability criteria</topic><topic>Stability regions</topic><topic>Sufficient conditions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cahlon, Baruch</creatorcontrib><creatorcontrib>Schmidt, Darrell</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cahlon, Baruch</au><au>Schmidt, Darrell</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability criteria for certain third-order delay differential equations</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2006-04-15</date><risdate>2006</risdate><volume>188</volume><issue>2</issue><spage>319</spage><epage>335</epage><pages>319-335</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><coden>JCAMDI</coden><abstract>In this paper, we study the asymptotic stability of the zero solution of third-order linear delay differential equations of the form
y
‴
(
t
)
=
p
1
y
″
(
t
)
+
p
2
y
″
(
t
-
τ
)
+
q
1
y
′
(
t
)
+
q
2
y
′
(
t
-
τ
)
+
v
1
y
(
t
)
+
v
2
y
(
t
-
τ
)
,
where
p
1
,
p
2
,
q
1
,
q
2
,
v
1
and
v
2
are certain constants. Here
τ
>
0
is a constant delay. In proving our results we make use of Pontryagin's theory for quasi-polynomials.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cam.2005.04.034</doi><tpages>17</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
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| ispartof | Journal of computational and applied mathematics, 2006-04, Vol.188 (2), p.319-335 |
| issn | 0377-0427 1879-1778 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_28753735 |
| source | Elsevier ScienceDirect Journals Complete; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Asymptotic stability Characteristic functions Delay Exact sciences and technology Integral equations Mathematical analysis Mathematics Ordinary differential equations Sciences and techniques of general use Stability criteria Stability regions Sufficient conditions |
| title | Stability criteria for certain third-order delay differential equations |
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