On necessary conditions for global asymptotic stability of equilibrium for the Liénard equation
In [1], necessary and sufficient conditions for the global asymptotic stability of the trivial solution of the Liénard equation ẍ + f ( x ) ẋ + g ( x )=0, g (0)=0, were obtained under the condition In [1], the following problem was also posed: To determine whether condition (A) is a necessary condit...
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| Veröffentlicht in: | Mathematical Notes 2013, Vol.93 (1-2), p.75-82 |
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| creator | Ignat’ev, A. O. Kirichenko, V. V. |
| description | In [1], necessary and sufficient conditions for the global asymptotic stability of the trivial solution of the Liénard equation
ẍ
+
f
(
x
)
ẋ
+
g
(
x
)=0,
g
(0)=0, were obtained under the condition
In [1], the following problem was also posed: To determine whether condition (A) is a necessary condition for the global asymptotic stability of the trivial solution of the Liénard equation. The present paper answers this question, and the answer is negative, i.e., condition (A) is not a necessary condition. |
| doi_str_mv | 10.1134/S0001434613010082 |
| format | Article |
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ẍ
+
f
(
x
)
ẋ
+
g
(
x
)=0,
g
(0)=0, were obtained under the condition
In [1], the following problem was also posed: To determine whether condition (A) is a necessary condition for the global asymptotic stability of the trivial solution of the Liénard equation. The present paper answers this question, and the answer is negative, i.e., condition (A) is not a necessary condition.</description><identifier>ISSN: 0001-4346</identifier><identifier>EISSN: 1573-8876</identifier><identifier>DOI: 10.1134/S0001434613010082</identifier><language>eng</language><publisher>Dordrecht: SP MAIK Nauka/Interperiodica</publisher><subject>Mathematics ; Mathematics and Statistics</subject><ispartof>Mathematical Notes, 2013, Vol.93 (1-2), p.75-82</ispartof><rights>Pleiades Publishing, Ltd. 2013</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2032-24c5797dbb3d38362ce473dd6a4d662d83bf653a986f4c045607aad32af6d6fd3</citedby><cites>FETCH-LOGICAL-c2032-24c5797dbb3d38362ce473dd6a4d662d83bf653a986f4c045607aad32af6d6fd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0001434613010082$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0001434613010082$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Ignat’ev, A. O.</creatorcontrib><creatorcontrib>Kirichenko, V. V.</creatorcontrib><title>On necessary conditions for global asymptotic stability of equilibrium for the Liénard equation</title><title>Mathematical Notes</title><addtitle>Math Notes</addtitle><description>In [1], necessary and sufficient conditions for the global asymptotic stability of the trivial solution of the Liénard equation
ẍ
+
f
(
x
)
ẋ
+
g
(
x
)=0,
g
(0)=0, were obtained under the condition
In [1], the following problem was also posed: To determine whether condition (A) is a necessary condition for the global asymptotic stability of the trivial solution of the Liénard equation. The present paper answers this question, and the answer is negative, i.e., condition (A) is not a necessary condition.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0001-4346</issn><issn>1573-8876</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp9UEtOwzAQtRBIhMIB2PkCAdvjOOkSVXwqReoCWAfHn-IqsYudLnIkzsHFSCg7JFYzo_fRm4fQNSU3lAK_fSaEUA5cUCCUkIqdoIwWJeRVVYpTlM1wPuPn6CKl3XRRQUmG3jYee6NMSjKOWAWv3eCCT9iGiLddaGWHZRr7_RAGp3AaZOs6N4w4WGw-DtPeRnfof-jDu8G1-_r0MuoZlLPTJTqzskvm6ncu0OvD_cvqKa83j-vVXZ0rRoDljKuiXJa6bUFDBYIpw0vQWkiuhWC6gtaKAuSyEpYrwgtBSik1MGmFFlbDAtGjr4ohpWhss4-un55qKGnmipo_FU0adtSkieu3Jja7cIh-ivmP6Btb-Wpg</recordid><startdate>2013</startdate><enddate>2013</enddate><creator>Ignat’ev, A. O.</creator><creator>Kirichenko, V. V.</creator><general>SP MAIK Nauka/Interperiodica</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2013</creationdate><title>On necessary conditions for global asymptotic stability of equilibrium for the Liénard equation</title><author>Ignat’ev, A. O. ; Kirichenko, V. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2032-24c5797dbb3d38362ce473dd6a4d662d83bf653a986f4c045607aad32af6d6fd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ignat’ev, A. O.</creatorcontrib><creatorcontrib>Kirichenko, V. V.</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematical Notes</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ignat’ev, A. O.</au><au>Kirichenko, V. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On necessary conditions for global asymptotic stability of equilibrium for the Liénard equation</atitle><jtitle>Mathematical Notes</jtitle><stitle>Math Notes</stitle><date>2013</date><risdate>2013</risdate><volume>93</volume><issue>1-2</issue><spage>75</spage><epage>82</epage><pages>75-82</pages><issn>0001-4346</issn><eissn>1573-8876</eissn><abstract>In [1], necessary and sufficient conditions for the global asymptotic stability of the trivial solution of the Liénard equation
ẍ
+
f
(
x
)
ẋ
+
g
(
x
)=0,
g
(0)=0, were obtained under the condition
In [1], the following problem was also posed: To determine whether condition (A) is a necessary condition for the global asymptotic stability of the trivial solution of the Liénard equation. The present paper answers this question, and the answer is negative, i.e., condition (A) is not a necessary condition.</abstract><cop>Dordrecht</cop><pub>SP MAIK Nauka/Interperiodica</pub><doi>10.1134/S0001434613010082</doi><tpages>8</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0001-4346 |
| ispartof | Mathematical Notes, 2013, Vol.93 (1-2), p.75-82 |
| issn | 0001-4346 1573-8876 |
| language | eng |
| recordid | cdi_crossref_primary_10_1134_S0001434613010082 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Mathematics Mathematics and Statistics |
| title | On necessary conditions for global asymptotic stability of equilibrium for the Liénard equation |
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