{"docId":9527,"paperId":9527,"url":"https:\/\/cm.episciences.org\/9527","doi":"10.2478\/cm-2021-0008","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":647,"name":"Volume 29 (2021), Issue 1 (Special Issue: Ostrava Mathematical Seminar)"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-03665010","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-03665010v1","dateSubmitted":"2022-05-11 15:42:25","dateAccepted":null,"datePublished":"2021-04-30 00:00:00","titles":{"en":"The inverse problem in the calculus of variations: new developments"},"authors":["Do, Thoan","Prince, Geoff"],"abstracts":{"en":"We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of n second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas\u2019s famous solution for n = 2. We then examine a new class of solutions in arbitrary dimension n and give some non-trivial examples in dimension 3."},"keywords":[["General Mathematics"],"[MATH]Mathematics [math]"]}