INTRODUCTION
xi
The lecture notes of Jon Jacobsen and Padilla have very strong links. Jon
Jacobsen explains in a very clear manner the study of non-linear problems by using
adequate versions of the Implicit Function Theorem. He mainly deals with the so
called Liouville-Gelfand problem. This is a non-linear problem which appears in the
study of combustible gas dynamics and consists in a non -linear differential equation
with a parameter. In order to study the existence of solutions of this problem,
the multiplicity of the parameter and bifurcation properties, Jacobsen includes
three sections to explain Implicit Function Theorems in lR
~,
partial differential
equations and the Implicit Function Theorem in Banach spaces, degree theory and
a globalization of the Implicit Function Theorem. Then he applies these ideas to
the Liouville-Gelfand problem and to the non-linear problem so called k-Hessian
equations.
We thank the authors for their excellent lectures and thier contribution to this
volume. We would also want to thank the sponsors of this School for financial
support:
a) Universidad Nacional Aut6noma de Mexico through the proyects PAEP
22003, PAPIIT IN102998 and the Facultad de Ciencias (graduate school in math-
ematics); b) CONACyT, proyect 32146-E; c) Proyecto universitario de fen6menos
nolineales y mecanica (FENOMEC).
Finally we appreciate the effort of the American and Mexican Mathematical
Societies to make this publication possible.
Salvador Perez-Esteva and Carlos Villegas-Blas
The Editors
Cuernavaca, Morelos, Mexico
UNIVERSIDAD NACIONAL AUTONOMA DE MEXICO, INSTITUTO DE
MATEMATICAS, UNIDAD CUERNAVACA, A.P. 273-3, ADMON. 3, CUER-
NAVACA, MORELOS 62251, MEXICO.
E-mail address: salvadormatcuer. unam.mx
E-mail address: villegasmatcuer.unam.mx
Previous Page Next Page