Author(s): Minhós, Feliz ; Oliveira, N
Date: 2022
Persistent ID: http://hdl.handle.net/10174/31306
Origin: Repositório Científico da Universidade de Évora
Subject(s): 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.
