{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T15:54:43Z","timestamp":1786982083352,"version":"3.56.0"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T00:00:00Z","timestamp":1690416000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T00:00:00Z","timestamp":1690416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math.Comput.Sci."],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1007\/s11786-023-00567-6","type":"journal-article","created":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T07:02:17Z","timestamp":1690441337000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Integrable Cases of the Polynomial Li\u00e9nard-type Equation with Resonance in the Linear Part"],"prefix":"10.1007","volume":"17","author":[{"given":"Victor F.","family":"Edneral","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,7,27]]},"reference":[{"key":"567_CR1","first-page":"119","volume":"25","author":"AD Bruno","year":"1971","unstructured":"Bruno, A.D.: Analytical form of differential equations (I, II). Trudy Moskov. Mat. Obsc. 25, 119\u2013262 (1971)","journal-title":"Trudy Moskov. Mat. Obsc."},{"key":"567_CR2","first-page":"199","volume":"26","author":"AD Bruno","year":"1972","unstructured":"Bruno, A.D.: Analytical form of differential equations (I, II). Trudy Moskov. Mat. Obsc. 26, 199\u2013239 (1972). ((in Russian))","journal-title":"Trudy Moskov. Mat. Obsc."},{"key":"567_CR3","first-page":"131","volume":"25","author":"AD Bruno","year":"1971","unstructured":"Bruno, A.D.: Analytical form of differential equations (I, II). Trans. Moscow Math. Soc. 25, 131\u2013288 (1971)","journal-title":"Trans. Moscow Math. Soc."},{"key":"567_CR4","first-page":"199","volume":"26","author":"AD Bruno","year":"1972","unstructured":"Bruno, A.D.: Analytical form of differential equations (I, II). Trudy Moskov. Mat. Obsc. 26, 199\u2013239 (1972). ((in English))","journal-title":"Trudy Moskov. Mat. Obsc."},{"key":"567_CR5","unstructured":"Bruno, A.D.: Local Method for Nonlinear Analysis of Differential Equations. Nauka, Moscow (1979). p. 254 ((in Russian))"},{"key":"567_CR6","doi-asserted-by":"crossref","unstructured":"Bruno, A.D.: Local Methods in Nonlinear Differential Equations. Translated by W.\u00a0Hovingh and S.\u00a0Coleman, p. 348. Springer, Berlin, Heidelberg (1989)","DOI":"10.1007\/978-3-642-61314-2"},{"key":"567_CR7","doi-asserted-by":"crossref","unstructured":"Bruno, A.D., Edneral, V.F., Romanovski, V.G.: On new integrals of the Algaba\u2013Gamero\u2013Garcia system. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2017, vol. 10490, pp. 40\u201350. Springer Series: LNCS (2017)","DOI":"10.1007\/978-3-319-66320-3_4"},{"key":"567_CR8","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/BF01208503","volume":"36","author":"D Hilbert","year":"1890","unstructured":"Hilbert, D.: \u00dcber die theorie der algebraischen Formen. Math. Ann. 36, 473\u2013534 (1890)","journal-title":"Math. Ann."},{"issue":"23","key":"567_CR9","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/S0168-9002(03)00530-8","volume":"502","author":"VF Edneral","year":"2003","unstructured":"Edneral, V.F., Khanin, R.: Application of the resonant normal form to high-order nonlinear odes using Mathematica. Nucl. Instr. Methods Phys. Res., Sect. A: Accel., Spectrom., Detect. Assoc. Equip. 502(23), 643\u2013645 (2003)","journal-title":"Nucl. Instr. Methods Phys. Res., Sect. A: Accel., Spectrom., Detect. Assoc. Equip."},{"issue":"901\u2013912","key":"567_CR10","first-page":"946","volume":"23","author":"A Li\u00e9nard","year":"1928","unstructured":"Li\u00e9nard, A.: Etude des oscillations entretenues. Rev. G\u00e9n. l\u2019\u00e9lectr. 23(901\u2013912), 946\u2013954 (1928)","journal-title":"Rev. G\u00e9n. l\u2019\u00e9lectr."},{"issue":"2","key":"567_CR11","first-page":"201","volume":"12","author":"LA Cerkas","year":"1977","unstructured":"Cerkas, L.A.: Conditions for a Li\u00e9nard equation to have a center. Differ. Equ. 12(2), 201\u2013206 (1977)","journal-title":"Differ. Equ."},{"issue":"1","key":"567_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jde.2004.01.008","volume":"200","author":"C Christopher","year":"2004","unstructured":"Christopher, C., Devlin, J.: On the classification of Li\u00c3nard systems with amplitude-independent periods. J. Differ. Equ. 200(1), 1\u201317 (2004)","journal-title":"J. Differ. Equ."},{"key":"567_CR13","doi-asserted-by":"publisher","first-page":"888","DOI":"10.1016\/j.amc.2018.07.056","volume":"339","author":"A Ruiz","year":"2018","unstructured":"Ruiz, A., Muriel, C.: On the integrability of Li\u00e9nard I-type equations via $$\\lambda $$-symmetries and solvable structures. Appl. Math. Comput. 339, 888\u2013898 (2018)","journal-title":"Appl. Math. Comput."},{"key":"567_CR14","unstructured":"The file Systems123.pdf: https:\/\/disk.yandex.ru\/d\/hu80Y8zZD1yznA"},{"key":"567_CR15","first-page":"803","volume-title":"Handbook of Exact Solutions for Ordinary Differential Equations","author":"AD Polyanin","year":"2003","unstructured":"Polyanin, A.D., Zaitsev, V.F.: Handbook of Exact Solutions for Ordinary Differential Equations, 2nd edn., p. 803. CRC Press, Chapman & Hall (2003)","edition":"2"}],"container-title":["Mathematics in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-023-00567-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11786-023-00567-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-023-00567-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T08:36:30Z","timestamp":1702370190000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11786-023-00567-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,27]]},"references-count":15,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["567"],"URL":"https:\/\/doi.org\/10.1007\/s11786-023-00567-6","relation":{},"ISSN":["1661-8270","1661-8289"],"issn-type":[{"value":"1661-8270","type":"print"},{"value":"1661-8289","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,27]]},"assertion":[{"value":"15 October 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 May 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 July 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"19"}}