Programa de Doutoramento em Matemática
Sistemas de equações diferenciais acoplados não lineares de ordem superior em intervalos limitados ou não limitados
Robert de Sousa

Orientação:  Feliz Manuel Barrão Minhós

The Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of the nonlinear differen-tial equations with full nonlinearities are scary and have gap in literature. The present work modestly try to fill this gap.

The systems covered in the work are essentially of the second-order (except for the first chapter of the first part) with boundary constraints either in bounded or unbounded intervals presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic).

The existence, and in some cases, the localization of the solu-tions is carried out in of Banach space and norms considered, fo-llowing arguments and approaches such as: Schauder’s fixed-point theorem or of Guo–Krasnosel’ski˘ı fixed-point theorem in cones, allied to Green’s function or its estimates, lower and upper solu-tions, convenient truncatures, the Nagumo condition presented in different forms, concept of equiconvergence, Carath´eodory func-tions and sequences.

On the other hand, parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on the physics, mechanics, bio-logy, forestry, and dynamical systems.

Keywords: Coupled systems, Bounded and unbounded intervals, Lower and upper solutions, Nagumo condition, Green’s functions, Fixed point theory.