{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:20:46Z","timestamp":1760235646269,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,9,11]],"date-time":"2021-09-11T00:00:00Z","timestamp":1631318400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This work concerns with the solvability of third-order periodic fully problems with a weighted parameter, where the nonlinearity must verify only a local monotone condition and no periodic, coercivity or super or sublinearity restrictions are assumed, as usual in the literature. The arguments are based on a new type of lower and upper solutions method, not necessarily well ordered. A Nagumo growth condition and Leray\u2013Schauder\u2019s topological degree theory are the existence tools. Only the existence of solution is studied here and it will remain open the discussion on the non-existence and the multiplicity of solutions. Last section contains a nonlinear third-order differential model for periodic catatonic phenomena, depending on biological and\/or chemical parameters.<\/jats:p>","DOI":"10.3390\/axioms10030222","type":"journal-article","created":{"date-parts":[[2021,9,12]],"date-time":"2021-09-12T21:45:57Z","timestamp":1631483157000},"page":"222","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Periodic Third-Order Problems with a Parameter"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7485-2500","authenticated-orcid":false,"given":"Feliz","family":"Minh\u00f3s","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Escola de Ci\u00eancias e Tecnologia, Instituto de Investiga\u00e7\u00e3o e Forma\u00e7\u00e3o Avan\u00e7ada, Universidade de \u00c9vora, Rua Rom\u00e3o Ramalho, 59, 7000-671 \u00c9vora, Portugal"},{"name":"Centro de Investiga\u00e7\u00e3o em Matem\u00e1tica e Aplica\u00e7\u00f5es (CIMA), Instituto de Investiga\u00e7\u00e3o e Forma\u00e7\u00e3o Avan\u00e7ada, Universidade de \u00c9vora, Rua Rom\u00e3o Ramalho, 59, 7000-671 \u00c9vora, Portugal"}]},{"given":"Nuno","family":"Oliveira","sequence":"additional","affiliation":[{"name":"Centro de Investiga\u00e7\u00e3o em Matem\u00e1tica e Aplica\u00e7\u00f5es (CIMA), Instituto de Investiga\u00e7\u00e3o e Forma\u00e7\u00e3o Avan\u00e7ada, Universidade de \u00c9vora, Rua Rom\u00e3o Ramalho, 59, 7000-671 \u00c9vora, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/BF02412022","article-title":"On the inversion of some differentiable mappings with singularities between Banach spaces","volume":"93","author":"Ambrosetti","year":"1972","journal-title":"Ann. 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