Nolinear Functional Analysis and Applications

Code: MAT11696D

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese

Sustainable Development Goals

4. Educação de qualidade - Assegurar a educação inclusiva, e equitativa e de qualidade, e promover oportunidades de aprendizagem ao longo da vida para todos.

Learning Goals

The main goal is to place students in contact with some methods and techniques of nonlinear functional analysis, as well as some of its applications to boundary value problems. Thus the student will make a first approach to this area of nonlinear analysis and obtain technical skills to make research in this field and related topics.
The applications to current problems in different and varied issues still open, allow the students to be engage with cutting-edge themes that, somehow, are at the frontier of knowledge.

1. Linear Functional Differential Equations : with delay and neutral . Existence , uniqueness and continuous dependence on parameters .
2 . Equations in Spaces of Finite Dimension and Applications
Green operator . Problem of multipoints.
Impulsive problems of higher order
3 . Oscillation of Functional Differential Equations
Nonlinear differential equations with delays.Teoremas Comparison and oscillation. Existence of non- oscillatory solutions .
4 . Impulsive Functional Problems and Stability
Lyapunov functions . Stability of solutions. Theorems on limits . Global stability relative to a parameter. Applications .
5 . Methods for Functional Value Problems on the Boundary. Equations with monotone operators . Iterative methods . Reduction equations . Method of lower and upper solutions
6 . Generalized Functional problems : adapted classical methods
Existence and multiplicity of solutions. Higher-order functional problems . Extremal solutions .