RCAAP Repository

In this work, we study a fixed point theorem for increasing operators in ordered normed spaces and we apply it in order to obtain results of existence of weak solution for semilinear elliptic equations of type 8<: ---u = f(x; u) + h; in u = 0; on @ ; where - RN is a smooth domain, f : -R --! R satisfies some convenient conditions and h 2 H--1(.

The notion of lineability emerged in the eighties, albeit its essence is quite older, as a method to measure the existence of linear structures in a priori nonlinear frameworks. More precisely, a subset of a topological vector space is lineable (spaceable) if it contains, except eventually for the null vector, an infinite-dimentional subspace (infinite- dimensional closed subspace). In this work we investigate lineability and spaceability in the context of norm attaining operators and sequence spaces.

In this paper we studied surfaces with constant mean curvature and surfaces with constant Gaussian curvature in the Sol space which are invariant under the action of two one-parameter subgroups of isometries of the ambient space. Furthermore, we classify the surfaces that satisfy a relationship of type k1 = mk2, where k1 and k2 are the principal curvatures of the surface and m &#8712; R.

We have as main issue in this work the Hierarchical Control, which consists in a leader-followers system. We studied in special the heat equation approximate controllability under Stackelberg-Nash&#146;s strategy, which is directed in controlling every system from local controls choices with the minimum possible costs.

The goal of our work is to prove the existence of solutions to a class of semilinear elliptic equations in a bounded domain, involving concave-convex type nonlinearities. We use a variety of methods to and these solutions, such as Mountain Pass Theorem, Ekeland's Variational Principle, Lagrange Multipliers Theorem, Nehari Manifold and sub and supersolution method.

In this work we study a class of semilinear equations of the logistic type. More precisely, we consider the homogeneous and inhomogeneous cases. In the homogeneous case, we discuss the existence, nonexistence and uniqueness of positive solution as well the decay at infinity. The existence is obtained by using the method of sub-super solutions. In the inhomogeneous case, we discuss the existence of positive solution and show that the decay at infinity is not exponential. The existence is obtained by using minimizes arguments, more precisely, the Direct Method of Calculus of Variations.

This work presents a study of Cohen strongly summing operators under the viewpoint of the theory of multilinear operators ideals and polynomial ideals. Furthermore, we introduce two new classes that generalize the concept of multilinear operators and polynomials of this nature, namely multiple Cohen strongly summing operators and Cohen strongly summing operators at a given point. We show that the new classes defined, as well as the previous classes, form normed ideals of operators/polynomials and that the class of multiple Cohen strongly summing operators forms a Banach ideal. We also show that the construction of the class of multiple Cohen strongly summing operators provides a holomorphy type and a coherent and compatible sequence of ideals.

In this work we study implicit differential equations. Following the Thom tranversality theorem and the singularity theory we find an open and dense subset of this equation class that present only good singularity. This singularity are of six kind well folded saddle, well folded node, well folded focus, elliptical gather, hyperbolic gather. Davydov,in [8] showed the normal forms of a IDE in the case of well folded saddle, well folded node, well folded focus. In the case of gathered singularities, Davydov showed that the normal forms of IDE contains functional moduli. For a special class of implicit differential equation, the binary differential equation (BDE), we study the normal forms in the case in that the discriminant is a Morse function.

In this work we study systems of elliptic equations of gradient and hamiltonean types by variational methods whose domains is the whole RN. More specifically, we use critical point theorems of the mountain pass and linking types to prove results of existence of non-trivial solutions to these problems.

The teaching of Complex Numbers is based almost exclusively on an algebraic approach, although the geometric approach of complex numbers is contemplated in the study of its polar form (or trigonometric). The purpose of this paper is to present some significant applications of complex numbers in plane geometry, making thus a contrast to this view strictly algebraic and formal, that has traditionally characterized the teaching of these numbers. We'll cover some classical theorems of geometry and some geometric problems, evaluating the efficiency of complex numbers as a tool to demonstrate the theorems and results relevant to the resolution of such problems. Some of the theorems selected in our study were: Napoleon's Theorem, the Circle of Nine Points and Simson Line.

In this work, our main objective is to introduce and investigate certain properties of the so-called primitive ideals of Pellikaan-Siersma, including a version relative to a pair of ideals and a generalization to higher order due to Jiang-Simis, as well as to apply such theory to the study of the conormal module M of an ideal in a quotient ring, with focus on an adequate description of its torsion part T(M) and on the freeness of the torsion-free module M=T (M). The connection between M and the second symbolic power of a certain ideal (the ideal whose conormal module is M) will also be highlighted.

The Makar-Limanov invariant ML(B) of an a-ne k-algebra B (with k a -eld, which will be typically assumed to be of characteristic zero) is a very important invariant, defined in terms of the kernels of suitable derivations of B called locally nilpotent derivations. The theme has connections to various central problems in Commutative Algebra, for instance, the Jacobian Conjecture, the Fourteenth Hilbert's Problem, and the Cancellation Problem, and has been investigated by many authors. In this work, after the presentation of basic concepts and results, our main goal is the explicit obtainment of the structure of ML(B) (as a k-algebra) when B is the coordinate ring of certain special a-ne algebraic hypersurfaces, to wit, the so-called Danielewski surfaces, as well as the famous Makar-Limanov 3-fold defined by x + x2y + z2 + t3 = 0.

This work presents a research on problems of maxima and minima of the Euclidean geometry. Initially we present some preliminary results followed by statements that in essence use basic concepts of geometry. Below are some problems of maximizing area and minimizing perimeter of triangles and convex polygons, culminating in a proof of the isoperimetric inequality for polygons and review the general case. Solve some classical problems of geometry that are related to outliers and present other problems as proposed.

In this work we discuss the concepts and definitions that construct Clifford algebras focusing on a introduction the theory Spin Geometry. That s because the connection this two subject, enabling such algebras know the measure that helps to understand the definition of spin manifold, concept introductory the this special topic in Riemannian Geometry. We begin with the construction of Clifford algebras associated to infinite dimensional vector spaces, over any field, passing to associated with finite dimensional. we see the spinores groups, Pin and Spin, which characterize and show the relation with the twisted adjoint representation, homomorphism that, when restricted to these groups, has an important role in defining of a spin structure. As this definition works with representations of real Clifford algebras, restricted to spinors groups such algebras, we introduced them for soon afterwards consider such representations. We concluded approaching the necessary theory for us to show that those groups are also Lie groups (where we urged an intersection with the analysis) and double covering, to complete the concepts algebraic present in the definition of spin manifold.

We present the own mathematic formalism to, first of all, study the holonomy interpretations of the adiabatic geometric phase presented by Berry-Simon and Aharanov-Anadan and, after this, the similirities found with the theory of representation groups, particularly, with the Borel-Weil-Bott theorem. These relations are made through classification of complex bundle line, and these results are used to introduce a cranked Hamiltonian. In general, we also show that the parameter space is a flag manifold or a submanifold of her and present a topologic argument of this space that indicates the relation between the structure Riemannian and the Berry s connection.

Neste trabalho provamos o Teorema algebro-geométrico de Ganey, o qual caracteriza completamente as condições de Whitney de famílias de espaços analíticos complexos com singularidades arbitrárias em termos do fecho integral de módulos naturalmente associados a estas famílias.

We start studing semi-stable solutions for the equation u = f(u) in a smooth and bounded domain of Rn, 2 n 4. The presented result is a L1 boundedness, which holds for all semi-stable positive solution and all non-linearity f. We also show a approach about the case u = f(u) in the unitary ball of Rn. The results obtained are Lq and Wk;q estimates for semi-stable radial solutions u 2 H1 0 , the proof of a boundedness if n 9 and, in case that g is increasing and convex, u 2 W3;2 in all dimension n.

In this paper, we study questions related to the existence and multiplicity of solutions to problems of Ambrosetti-Prodi type. We present the conjecture of Lazer- McKenna, checking its validity in the one dimensional case. To obtain our results, we use essentially topological, variational and sub and supersolution methods.

In this work, we obtain existence, nonexistence and multiplicity of solutions for the elliptic partial differential equation u 1 2 (x:ru) + "jujp1u = u; x 2 RN; where N 3, " = 1, > 0 and 1 < p (N + 2)=(N 2). Such equation is obtained when we look for self-similar solutions for certain nonlinear heat equations. To obtain the main results, we use variational methods, more precisely, minimization arguments, Lagrange multipliers theorem and elliptic regularity results.

Here we study a class of semilinear elliptic equations with nonlinearity of an inverse square type. This equations arise, in applications, on the modeling of certain electrostatic devices from microtechnology, MEMS - Micro Electro Mechanical Systems. More precisely, these equations characterizes the function that represents the deformation of a deformable capacitor under the influence of an applied voltage. The Mathematical tools used on the study of such problems involve a bit of Nonlinear Analysis and Partial Differential Equations' methods as sub and supersolutions, sign preserving Theorems (Maximum Principle, Boggio's Principle), energy estimates via Sobolev spaces, etc. In a parallel way we wish to emphasize the importance of this investigation, in Mathematics, on helping the understanding on the class of singular problems in Partial Differential Equations.