NSA-UPRH Regional Conference on Global Continuation Methods

Abstracts of Main Lectures

1. Introduction to Topics in Nonlinear Analysis (2 lectures)}: These lectures will introduce the basics of degree theory, and global and local bifurcation (in the sense of Rabinowitz).

2. Introduction to Nonlinear Elastostatics (2 lectures)}: Here we will study the formulation of the boundary value problem of nonlinear elastostatics, the formal theory of stationary potential energy, and the constitutive theory of elastic materials.

3. Global Continuation in Displacement Problems (1 lecture)}: We will study how to apply the Leray-Schauder degree theory to the pure displacement problem of equilibrium in nonlinear elasticity.

4. A Generalized Degree (2 lectures)}: In these lectures we are going to study the complementing condition and how to use it to obtain a--priori estimates. We will also study the definition and properties of the generalized degree mentioned above in the project description, together with the three key concepts of properness, Fredholm operators, and spectral estimates.

5. Global Continuation and Global Bifurcation in Nonlinear Elastostatics (2 lectures)}: Here we will study how to apply the new degree, discussed in the previous two lectures, to problems in nonlinear elastostatics. We will discuss both, general theory and concrete applications.

6. Open Problems and New Directions (1 lecture)}: In this last lecture we will discuss some open and challenging problems in this area and new directions for important research problems.

We include below a link to a preliminary version of the lecture notes in pdf format. These notes are currently under revision and will be the basis for a monograph that will be sent for publication during the Spring of 2004. The final version of the lecture notes will include as well several of the papers presented at the conference.

Download pdf version of the lecture notes. (600KB approx.)