Periodic third-order problems with a parameter

• Autor(a) principal: Minhós, Feliz
• Data de Publicação: 2021
• Outros Autores: Oliveira, N
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10174/31306; https://doi.org/Minhós F, Oliveira N. Periodic Third-Order Problems with a Parameter. Axioms. 2021; 10(3):222. https://doi.org/10.3390/axioms10030222; https://doi.org/10.3390/axioms10030222
• topic: higher-order periodic problems; lower and upper solutions; Nagumo condition; degree theory; periodic catatonic phenomena

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–Schauder’s 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.