RCAAP Repository

In this work we study the Navier-Stokes equations in bounded domains of Rn. Initially we the case n = 2 and we show that its variational formulation is well put (in case the Hadamard). We show the existence of solution for the case n  4 . In both cases we use the Faedo-Galerkin method.

This work presents one global Carleman inequality for wave linear equation with bounded potential. Furthermore, we do two applications of this result. The first one refers to the study of exact controlabillity on the boundary and the second one deals with an inverse problem, where we want to recover the potential.

In this work, we will study the existence and multiplicity of weak solutions for a class of nonhomogeneous elliptic problems involving exponential growth Trudinger-Moser type in R2. For this, we will use the Ekeland s Variational Principle and the Mountain Pass Theorem without the Palais-Smale condition in combination with a version of the Trudinger-Moser inequality.

Our goal in this work is to present beautiful results due to Huckaba-Marley concerning the Hilbert coefficients of an ideal of finite co-length in a Cohen-Macaulay local ring, as well as the depth of its associated graded ring. For this end, we employ the Huckaba- Marley complex, which is a fundamental tool for the obtainment of the main theorem discussed herein.

We study the geometry of surfaces immersed in R4 through the singularities of their families of height functions. Inflection points on the surfaces are shown to be umbilic points from their families of height functions. Furthermore, we see that inflection points of imaginary type are isolated points of the curve --1(0). As a consequence we prove that any dive generic convexly embedded S2 in R4 has inflexion points.

This work is divided in two subjects. The first concerns about the Bohnenblust-Hille and Hardy- Littlewood multilinear inequalities. We obtain optimal and definitive generalizations for both inequalities. Moreover, the approach presented provides much simpler and straightforward proofs than the previous one known, and we are able to show that in most cases the exponents involved are optimal. The technique used is a combination of probabilistic tools and of an interpolative approach; this former technique is also employed in this thesis to improve the constants for vector-valued Bohnenblust-Hille type inequalities. The second subject has as starting point the existence of Peano spaces, that is, Haurdor spaces that are continuous image of the unit interval. From the point of view of lineability we analyze the set of continuous surjections from an arbitrary euclidean spaces on topological spaces that are, in some natural sense, covered by Peano spaces, and we conclude that large algebras are found within the families studied. We provide several optimal and definitive result on euclidean spaces, and, moreover, an optimal lineability result on those special topological vector spaces.

In this work, we study existence, non-existence and multiplicity results of nodal solutions for the nonlinear Schrödinger equation (P) -u + V (x)u = f(u) in ; where is a smooth domain in R2 which is not necessarily bounded, f is a continuous function which has exponential critical growth and V is a continuous and nonnegative potential. In the first part, we prove the existence of least energy nodal solution in both cases, bounded and unbounded domain. Moreover, we also prove a nonexistence result of least energy nodal solution for the autonomous case in whole R2. In the second part, we establish multiplicity of multi-bump type nodal solutions. Finally, for V - 0, we prove a result of infinitely many nodal solutions on a ball. The main tools used are Variational methods, Lions's Lemma, Penalization methods and a process of anti-symmetric continuation.

In this work we study questions related to the existence of positive solutions for some classes of quasilinear Schrödinger equations, with hypotheses on the potential that permit this potential to vanish at infinity. In order to use variational methods to obtain our results, we make some changes of variables to obtain some semilinear equations, whose associated functionals are well defined in a classical Sobolev spaces. We also work with these equations on an Orlicz type space whose energy functional satisfy the geometric properties of the Mountain Pass Theorem. We still use the penalty technique due to Del Pino and Felmer and the Moser iteration method to obtain estimates in L1 norm, which are fundamental to our study.

In this work we studied existence of positive solutions for an elliptic problem with critical Sobolev exponent (-u = up + f(x; u) em u = 0 sobre @ that vanishes on the boundary of a bounded domain of Rn. The nonlinearity f(x; u) has subcritical growth. This is done by showing that the minimax level is below a constant that depends only on the dimension of the domain and the best Sobolev constant.

Cook's local infuence approach based on normal curvature is an important diagnostic tool for assessing local infuence of minor perturbations to a statistical model. However, no rigorous approach has been developed to address two fundamental issues: the selection of an appropriate perturbation and the development of infuence measures for objective functions at a point with a nonzero first derivative. The aim of this paper is to develop a diferential-geometrical framework of a perturbation model (called the perturbation manifold) and utilize associated metric tensor and affine curvatures to resolve these issues. We will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model.

In this work we investigate, in detail, recent research works related to the theory of absolutely summing operators between Banach spaces. More precisely, we investigate the connection between the concept of cotype and coincidence results in the theory of absolutely summing operators.

In this work we study a recent unified version of Pietsch Domination Theorem, due to Botelho, Pellegrino and Rueda ([8]) that unifies a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p- summing linear operators. A final result shows that Pietsch-type domination theorems are totally free from algebraic conditions, such as linearity, multilinearity, etc.

In this work we talk about properties of the Dirichlet-to-Neumann map for the conductivity equation in a smooth manifold with boundary of R2. We use several times the Maximum Principle to conclude a Alternating Property of the Dirichlet-to- Neumann map. Using this property, we and that the Kernel satises a given set of inequalities. Finally, we note that these inequalities imply the Alternating Property of the Kernel of the Dirichlet-to-Neumann map.

We present in this work a complete classification of the sublattices of (Zn,+, ≥) which are not groups of divisibility. Thus we provide a new class of ordered filtered groups of which are not groups of divisibility. The sublattices presented here generalize the exemples of P.Jaffard and G. G. Bastos

In this work we'll prove existence of weak solutions to a coupled mixed problem of nonlinear partial diferential equation in the class of systems of nonlinear Klein- Gordon equations involving pseudo-Laplacian operator. For proving existence of weak solutions we use Faedo-Galerkin's method with compacity and monotonicity properties.

This work is dedicated to the study of existence, uniqueness and stability for the nonlinear equation for Kawahara ut + ux + uxxx + upux - uxxxxx = 0 (p = 1; 2) , on a bounded domain. To prove the existence and uniqueness, we use techniques of nite di¤erences for the case p = 1 and semigroup theory for the case p = 2. Under e¤ect of a localized damping mechanism, we obtain an exponential decay (as t ! 1) for the energy associated to solutions of Kawahara equation. Combining energy estimatives, multipliers and compacteness argument, the stabilization result was reduced to prove a unique continuation property for the Kawahara equation. This property was proved using a result due to J. C. Saut and B. Sheurer (see [38]).

In this work we investigate recent results involving lineability and spaceability and the nonlinear theory of absolutely summing mappings.

In this dissertation, we study existence of both one-sign and nodal positive solutions (with exactly two nodal domains) for a class of quasilinear Schrödinger equations, which model physic phenomena, for example, in plasma physics. To obtain the results, it was used, mainly, the Nehari method, as well as, regularity theory of elliptic and Concentration-Compactness Principle.

In this work we present results of existence, non-existence and uniqueness of radial positive solutions for elliptic semilinear equations in subdomains of euclidean plane. We consider nonlinearities involving critical growth the type Trudinger- Moser. The technique used is shooting method introduced in 1905 by Severini [21]. This is a iterative method which permits determine the solution of a contour problem by analysis of approximated solutions of a family of initial value problems generated by himself. For its iteractive caracter, the shooting method it has been used effectively in applied mathematics, for exemple in the computational mathematical, where specific algorithms are used to perform such interactions. Here in an abstract approach through analytic techniques of continuity we examined whether an iteration converges to a solution of the contour problem under study.

In this work we present some results involving lineability and the linear theory of absolutely summing operators. We note that the technique presented is closely related to the theory of hereditarily indecomposable Banach spaces and that the presence of an unconditional basis in one of the spaces involved is crucial to guarantee some results.