The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach
This paper is concerned with the problem of existence and uniqueness of solutions for the semilinear fourth-order differential equation uiv – ku′′ + a(x)u+c(x) f (u) = 0. Existence and uniqueness is proved using variational methods and maximum principles. We also give a dynamical system approach to t...
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EDP Sciences
2020-01-01
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| Series: | ITM Web of Conferences |
| Online Access: | https://www.itm-conferences.org/articles/itmconf/pdf/2020/04/itmconf_icamnm2020_03005.pdf |
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doaj-60d80c05172245dbb76e1b01dd53ea842021-04-02T20:26:10ZengEDP SciencesITM Web of Conferences2271-20972020-01-01340300510.1051/itmconf/20203403005itmconf_icamnm2020_03005The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approachDanet Cristian Paul0Department of Applied Mathematics University of CraiovaThis paper is concerned with the problem of existence and uniqueness of solutions for the semilinear fourth-order differential equation uiv – ku′′ + a(x)u+c(x) f (u) = 0. Existence and uniqueness is proved using variational methods and maximum principles. We also give a dynamical system approach to the equation. We study the bifurcation of the system and show that the behaviour of the stationary points S (α, 0, 0, 0) depend on the relation between the parameter k and β = f ′(α).https://www.itm-conferences.org/articles/itmconf/pdf/2020/04/itmconf_icamnm2020_03005.pdf |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Danet Cristian Paul |
| spellingShingle |
Danet Cristian Paul The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach ITM Web of Conferences |
| author_facet |
Danet Cristian Paul |
| author_sort |
Danet Cristian Paul |
| title |
The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach |
| title_short |
The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach |
| title_full |
The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach |
| title_fullStr |
The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach |
| title_full_unstemmed |
The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach |
| title_sort |
study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach |
| publisher |
EDP Sciences |
| series |
ITM Web of Conferences |
| issn |
2271-2097 |
| publishDate |
2020-01-01 |
| description |
This paper is concerned with the problem of existence and uniqueness of solutions for the semilinear fourth-order differential equation uiv – ku′′ + a(x)u+c(x) f (u) = 0. Existence and uniqueness is proved using variational methods and maximum principles. We also give a dynamical system approach to the equation. We study the bifurcation of the system and show that the behaviour of the stationary points S (α, 0, 0, 0) depend on the relation between the parameter k and β = f ′(α). |
| url |
https://www.itm-conferences.org/articles/itmconf/pdf/2020/04/itmconf_icamnm2020_03005.pdf |
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AT danetcristianpaul thestudyofafourthorderdifferentialequationexistenceuniquenessandadynamicalsystemapproach AT danetcristianpaul studyofafourthorderdifferentialequationexistenceuniquenessandadynamicalsystemapproach |
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