Proceedings of the USA-Chile Workshop on Nonlinear Analysis

The joint USA-Chile Workshop on Nonlinear Analysis took place at the University Federico Santa Maria, Viña del Mar-Valparaiso, Chile, on January 10 - 15, 2000. This is the second of these meetings; the first was held in April 1985 in Santiago.

The organizing committee consisted of the following members: Patricio Felmer, Manuel Del Pino, and Raul Manasevich from the University of Chile; Paul Rabinowitz from the University of Wisconsin; and Elias Tuma from the University Federico Santa Maria.

The workshop was aimed at researchers, graduate students, and advanced undergraduate students working in various areas of Nonlinear Analysis, Differential Equations, and their applications. More than one hundred participants from more than twenty countries gathered together for the event.

During the meeting there were 50-minute plenary talks in the mornings and 30-minute talks in the afternoons. There were also sessions for graduate students to describe briefly their results.

Plenary talks were delivered by the following speakers: Abbas Bahri, Rafael Benguria, Alfonso Castro, David Costa, Michael Crandall, Lawrence Evans, Manuel del Pino, Patricio Felmer, Djairo de Figueiredo, Yanyan Li, Paul Rabinowitz, James Serrin, William Troy, Gunther Uhlmann, Laurent Veron, and Zhi-Qiang Wang. The list of the talks presented at the workshop is as follows:

• Amandine Aftalion, France, On the symmetry of solutions of the Ginzburg-Landau equations for small domains
• Pablo Amster, Argentina, Nonlinearities for a second order ODE
• Andres Avila, Brazil, Stability of the Faber-Krahn inequality and Payne-Polya-Weinberger inequality on Sⁿ
• Abbas Bahri, USA, $L^\infty$ bounds and Morse indices for solutions of superlinear elliptic PDE's
• Rafael Benguria, Chile, A simple proof of a theorem of Laptev and Weidl
• Marie-Françoise Bidaut-Veron, France, Integral estimates and nonexistence results for nonlinear elliptic systems
• Jerome Busca, France, Elliptic estimates for systems and applications
• Anna Capietto, Italy, On a boundary-value problem associated to a system of second order ordinary differential equations
• Alfonso Castro, USA, Sign-changing solutions for elliptic boundary-value problems
• Sui Sun Cheng, Taiwan, On a nonlinear difference boundary-value problem
• Vicente Chicaiza, Ecuador, The Rosenau equation with nonlinearities
• Martin Chuaqui, Chile, A hyperbolic system in the hyperbolic plane
• Carlos Cid, Chile, On static solutions of a Lorentz invariant equation in dimension 3
• Carmen Cortazar, Chile, The problem of uniqueness of the limit in a reaction diffusion equation
• David Costa, USA, Some theoretical and computational aspects of superlinear elliptic problems
• Vittorio Coti Zelati, Italy, Heteroclinic solutions between stationary points at different energy levels
• Michael Crandall, USA, A remark on infinity harmonic functions
• Michel Cure, Chile, Non-linear differential equation for radiation driven winds from hot stars
• Walter Dambrosio, Italy, On the existence of unbounded solutions to an asymmetric perturbed oscillator
• Juan Davila, USA, Some results concerning the extremal solution of a nonlinear elliptic equation with a parameter
• Djairo Guedes de Figueiredo, Brazil, Recent results on the existence of solutions of nonlinear elliptic systems
• Pablo Luis De Napoli, Argentina, Some results about equations of p-Laplacian type. sumability of solutions in Lorentz spaces
• Manuel del Pino, Chile, On the location of the onset of superconductivity
• Jean Dolbeault, France, Local moving planes methods for semi-linear elliptic equations with non-lipschitz nonlinearities
• Pavel Drabek, Czech Republic, One dimensional p-Laplacian at the first eigenvalue - existence results of the Fredholm type
• Manuel Elgueta, Chile, Short time behavior near the boundary for the heat equation with a nonlinear boundary condition
• Maria J. Esteban, France, New variational methods in the description of the eigenvalues of operators with gaps
• Lawrence Evans, USA,
• Patricio L. Felmer, Chile, Spike layers in some singularly perturbed elliptic equations
• Marcelo Fernandes Furtado, Brazil, Multiplicity of solutions for a nonlinear problem at double resonance
• Julian Fernandez Bonder, Argentina, A new free boundary problem in combustion theory
• Cesar Flores, Chile, Blow-up rate for semilinear heat equation $u_1=\Delta u+V(x) +u^p$
• Isabel Flores, Chile, Ground states of semilinear elliptic equations: a geometric approach
• Marta Garcia-Huidobro C., Chile, Some results concerning the solutions to the b.v.p. $-(a(r)|u'|^{p-2}u') = b(r)|u|^{q-2}u$,\ $r\in (0,R)$ 1< p< q, $u(R) = 0$
• Jean-Pierre Gossez, Belgium, A nodal domain property for the p-Laplacian
• Ignacio Guerra, The Netherlands, Transport of reactive solutes induced by well injection in R³: constant flow rate
• Chaitan P. Gupta, USA, Multiple solutions for a super-linear three-point boundary-value problem
• Istvan Gyori, Hungary, Stability results in state dependent delay differential equations
• Michal Kowalczyk, USA, Diffusion mediated transport and the Brownian Ratchet
• Pawel Kroeger, Chile, On the ranges of eigenfunctions of the Laplacian
• Enrique Lami Dozo, Argentina, A Holderian elliptic problem related to conical-type singularities
• Claudia Lederman, Argentina, A mixed semilinear parabolic problem in a non-cylindrical space-time domain
• Sebastian Lorca, Brazil, Existence of non-radial solutions of an Euclidean scalar field equation in a subspaces of $H^1$ with compact properties
• Yanyan Li, USA, Estimates for elliptic systems from composite material
• Peter A. Markowich, Austria, Nonlinear (convection-) diffusion equations, asymptotics of kinetic equations and convex Sobolev inequalities
• Salome Martinez, USA, The effect of diffusion and cross-diffusion in the 3X3 Lotka Volterra competition system
• Juan Molina, Chile, Morse index estimates for strongly indefinite functionals with (PS)
• Raul Naulin, Venezuela, Unstable delay systems
• Jaime H. Ortega, Chile, Some results on controllability for linear and non-linear systems
• Axel Osses, Chile, Controllability and homogenization of a semilinear elliptic problem in an hypersurface
• Patrizia Pucci, Italy, A strong maximum principle and a compact support principle for elliptic differential inequalities
• Mahmoud Qafsaoui, France, Equivalence between regularity theorems and heat kernels estimates for higher order elliptic operators (and systems) under divergence form
• Alexander Quaas, Chile, Strong maximum principle and compact support principle for elliptic equation and elliptic systems
• Paul Rabinowitz, USA, On a theorem of Strobel
• Miguel Ramos, Portugal, Superlinear problems involving the bilaplacian operator
• Andrejs Reinfelds, Latvia, Partial linearization and simplifying of impulsive differential equations
• Diego F. Rial, Argentina, The nonlinear Schrodinger equation
• Julio D. Rossi, Argentina, Existence for an elliptic System with nonlinear boundary conditions
• Mariel Saez T., Chile, On the extinction profile for solutions of $u_t=\Delta u^{N-2\over N+2}$
• Luis Sanchez, Portugal, Solutions in unbounded intervals for a nonautonomous ODE related to fisher's equation
• James Serrin, USA, Local behavior and Liouville theorems for quasilinear elliptic operators
• Elves A. B. Silva, Brazil, Multiple solutions for semilinear elliptic systems at resonance
• Panagiotis Souganidis, USA, Fully nonlinear stocastic PDE's
• Guido Sweers, The Netherlands, Sign change for the Green function and the first eigenfunction of clamped plate type equations
• Franciszek H. Szafraniec, Poland, A selection problem coming from unbounded subnormality
• William C. Troy, USA, Pattern formation in higher equations
• Pedro Ubilla L., Chile, The exact number of positive solutions for an elliptic equation with concave and convex nonlinearities
• Gunther Uhlmann, USA, The boundary distance function in inverse problems
• Antonio Jesus Ureña, Spain, Pendulum-like boundary-value problems with linear damping and homogeneous Dirichlet boundary conditions; some existence and multiplicity results
• Laurent Veron, France, Boundary trace of positive solutions of nonlinear equations
• Zhi-Qiang Wang, USA, On the Caffarelli-Kohn-Nirenberg inequalities
• Jianfu Yang, Brazil, On Schrodinger equation with periodic potential and critical Sobolev exponent
• Cecilia S. Yarur, Chile, Existence results of non-negative solutions for a Dirichlet problem
• Henghui Zou, USA, On the method of moving spheres for non-existence for cooperative semilinear elliptic systems

Special Issue Editors
Raul Manasevich
University of Chile
e-mail: manasevi@dim.uchile.cl

Paul Rabinowitz
University of Wisconsin
Madison, WI, USA.
rabinowi@math.wisc.edu