Claudianor O. Alves (Universidade Federal de Campina Grande)

Abstract: (14 KB)


Elves A. B. Silva (Departamento de Matemática, Universidade de Brasília) Existence of a positive solution for quasilinear
Schrödinger equations

Abstract: (32 KB)


Vieri Benci (Università di Pisa) Hylomorphic solitons for the KleinGordonMaxwell equations

Abstract: Roughly speaking a solitary wave is a solution of a field equation whose
energy travels as a localized packet and which preserves this localization in
time. A soliton is a solitary wave which exhibits some strong form of stability
so that it has a particlelike behavior. The solitons whose existence is related
to the ratio energy/charge are called hylomorphic. This class includes the Q
balls, which are spherically symmetric solutions of the nonlinear KleinGordon
equation, as well as the solitons which occur, by the same mechanism, in the
nonlinear Schroedinger equation. We will show that also the nonlinear Klein
GordonMaxwell equations admits hylomorphic solitons. This kind of soliton in
the physical literature are called charged Qballs.


Joao Marcos Bezerra do Ó (Universidade Federal da Paraíba)
A Sharp TrudingerMoser Type Inequality

Abstract: (13 KB)


Lucio Boccardo (Università di Roma 1)
Quasilinear and semilinear singular elliptic equations and systems

Abstract: (91 KB)


Alfonso Castro (Harvey Mudd College, Claremont) Wave equations with nonmonotone nonlinearity

Abstract: Recent results on existence of solutions to wave equations
with nonmonotone nonlinearity and
infinite dimensional kernel will be discussed. Loss of regularity due
to the interaction of the nonlinearity with
eigenvalues of infinite multiplicity will be presented.


Giovanna Cerami (Politecnico di Bari)
Multiple positive solutions for some Schröodinger Equations

Abstract: (20 KB)


Mónica Clapp (Universidad Nacional Autónoma de México)
Intertwining semiclassical solutions to a SchrödingerNewton system

Abstract: (45 KB)


David Costa (University of Nevada) On Positive Solutions for a Class of CaffarelliKohnNirenberg type Equations

Abstract: We consider solvability for a class of singular
CaffarelliKohnNirenberg type equations in R^N with a signchanging
weight function. In particular, we examine how the properties of the
Nehari manifold and the fibrering maps affect the question of
existence of positive solutions.


Arnaldo S. do Nascimento (Universidade Federal do Sao Carlos) Stable stationary solutions to a reactiondiffusion equation with zero Neumann boundary condition in rectangular domains.

Abstract: We prove existence of nonconstant stable stationary solutions of a
reactiondiffusion equation with no flux boundary condition in
rectangles and squares. By a wellknown result of Casten and
Holland and also Matano, such solutions do not exist in convex
domains which are at least C^2; we prove the same result under
weaker hypothesis on the regularity of the domain. In particular we
exhibit a C^1 convex domain for which this result still holds.
The approach is variational and based on Gammaconvergence
techniques. Symmetry inheritance from symmetry properties of the domain
and the reaction term is also obtained using the Unique Continuation
Principle. In particular for the square a complete geometric picture of
the level sets of the stable equilibria is obtained.


Marcelo F. Furtado (Universidade de Brasília)
Multiplicity and concentration of solutions for elliptic systems with vanishing potentials

Abstract: (31 KB)


Filippo Gazzola (Dipartimento di Matematica Politecnico di Milano) The first biharmonic Steklov eigenvalue: optimization and critical growth elliptic problems

Abstract: We study some properties of the first biharmonic Steklov eigenvalue.
We set up an optimal shape problem and we show its role in critical
growth semilinear elliptic problems.


JeanPierre Gossez (Univ. of Bruxelles) Maximum and antimaximum principles: beyond the frst eigenvalue

Abstract: (31 KB)


Norimichi Hirano (Yokohama National University)
Existence of Steady Stable Solutions for GinzburgLandau equation in a domain with nontrivial topology

Abstract: (37 KB)


Otared Kavian (Universite de Versailles) A Nonlinear Population Dynamics Model: Approximate Controllability by Birth Control using the Kakutani Fixed Point Theorem

Abstract: we analyse an approximate
controllability result for a nonlinear
population dynamics model. In this model the
birth term is nonlocal and describes the
recruitment process in newborn individuals
population, and the control acts on a small
open set of the domain and corresponds to an
elimination or a supply of newborn individuals.
In our proof we use a unique continuation
property for the solution of the heat equation
and the KakutaniFanGlicksberg fixed point theorem for multivalued operators.


Sebastián Lorca (UTA, Chile) Multiple solutions for the mean curvature equation

Abstract: (14 KB)


Liliane Maia (Departamento de Matemática, Universidade de Brasília, Brazil) Existence of antisymmetric solutions for a class
of nonlinear Schrödinger equations

Abstract: (44 KB)


Gianni Mancini (Università degli Studi ”Roma Tre”)
MoserTrudinger inequalities on conformal discs

Abstract: (65 KB)


Everaldo Souto de Medeiros (Universidade Federal da Paraìba)
Weak solutions of quasilinear elliptic systems via the cohomological index

Abstract: (26 KB)


Anna Maria Micheletti (Univ. di Pisa)
Some generic properties of non degeneracy of critical points

Abstract: (48 KB)


Olimpio Miyagaki (Universidade Federal de Juiz de Fora)
Existence results for quasilinear elliptic exterior problems involving convection term with nonlinear Robin boundary conditions

Abstract: (45 KB)


Marcelo Montenegro (Unicamp, Brazil) Concentrating solutions for an elliptic equation arising in free boundary problems

Abstract: (13 KB)


Filomena Pacella (Univ. Roma 1) Radial solutions of semilinear elliptic problems: spectral analysis and bifurcation

Abstract: We consider radial positive solutions of semilinear
elliptic problems with power nonlinearities either in an annulus or
in the exterior of a ball and show some results on the spectrum of
the linearized operator. From this we deduce on one side bifurcation
results, in particular with respect to the exponent of the nonlinear
term, on the other side existence of "quasiradial solutions" in
domains close to an annulus. All results apply also to the
supercritical case when the existence and multiplicity of
(nonradial) solutions seems particularly difficult to get.


Charles Stuart (Ecole Polytechnique Fédérale Lausanne)
Localization of PS and Cerami sequences in a mountain pass geometry

Abstract: (34 KB)


Gabriella Tarantello (Università di Roma Tor Vergata) Uniqueness and Symmetry results for solutions of a mean
field equation on s^2 via a new bubbling phenomenon

Abstract: Motivated by the study of gauge field vortices we consider a mean field
equation on the standard twosphere involving a Dirac distribution supported at a point P of S^2.
As needed for the applications, we show that solutions ”concentrate” exactly at P for some limiting value of a given parameter.
We use this fact to obtain symmetry (about the axis OP) and uniqueness property for the solution.
The presence of the Dirac measure makes such a task particularly delicate.
Indeed, we need to rule out the possibility that, after blow up (in a suitable scale), the solution sequence may admit a
double ”peak” profile described in terms of appropriate “limiting” problems.
For instance we need to account for the presence of nonaxially symmetric solutions in such ”limiting” problems.
In this process, we establish a symmetry result about a maximal circle through P and its antipodal point P*, that applies
to more general situations where the full axial symmetry cannot be expected.
This work is in collaboration with D. BARTOLUCCI and C.S. LIN.


Eduardo Teixeira (Univ. Federal Ceara) Existence and regularity theory for free boundary problems in Riemannian manifolds

Abstract: Physical models in Riemannian manifolds are central themes of
research within the modern theory of mathematical analysis. Problems with
unknown boundaries (free boundary problems), often employed to model
discontinuous change of phases, are of particular interest in this new set
up. In this talk, I will present some fine regularity tools, developed
together with Lei Zhang (Univ. Florida), in the study of free boundary
problems in nonEuclidean environments. Our results are generalizations of
the famous almostmonotonicity formulae of Caffarelli, Jerison and Kenig
(Ann Math 2002). Several applications will be delivered.


Susanna Terracini (Univ. Milano Bicocca) On some optimal partition problems

Abstract: We consider the free boundary problem associated with optimal
partitions related with linear and nonlinear eigenvalues. We are
concerned with extremality conditions and the regularity of the nodal
sets, also in connection with that of eigenfunctions and the number of
their nodal domains.


Pedro Ubilla (Universidad de Santiago de Chile)
Superlinear elliptic problems with sign changing coefficients

Abstract: (20 KB)

