MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS

This paper proves the multiplicity of positive solutions for the following class of quasilinear problems: {-epsilon(p)Delta(p)u+(lambda A(x) + 1)vertical bar u vertical bar(p-2)u = f(u), R(N) u(x)>0 in R(N), where Delta(p) is the p-Laplacian operator, N > p >= 2, lambda and epsilon are positive parameters, A is a nonnegative continuous function and f is a continuous function with subcritical growth. Here, we use variational methods to get multiplicity of positive solutions involving the Lusternick-Schnirelman category of intA(-1)(0) for all sufficiently large lambda and small epsilon.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Shape, transverse size, and charged-hadron multiplicity of jets in pp collisions at root s=7 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multiplicity of Boardman strata and deformations of map germs

We define algebraically for each map germ f: Kn, 0→ Kp, 0 and for each Boardman symbol i = (il, . . ., ik) a number ci(f) which is script A sign-invariant. If f is finitely determined, this number is the generalization of the Milnor number of f when p = 1, the number of cusps of f when n = p = 2, or the number of cross caps when n = 2, p = 3. We study some properties of this number and prove that, in some particular cases, this number can be interpreted geometrically as the number of Σi points that appear in a generic deformation of f. In the last part, we compute this number in the case that the map germ is a projection and give some applications to catastrophe map germs.

Multiplicity of solutions for a biharmonic equation with subcritical or critical growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Existence and multiplicity of solutions for a prescribed mean-curvature problem with critical growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

MULTIPLICITY OF NONRADIAL SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON ANNULUS WITH EXPONENTIAL CRITICAL GROWTH

In this paper, we establish the existence of many rotationally non-equivalent and nonradial solutions for the following class of quasilinear problems (p) {-Delta(N)u = lambda f(vertical bar x vertical bar, u) x is an element of Omega(r), u > 0 x is an element of Omega(r), u = 0 x is an element of Omega(r), where Omega(r) = {x is an element of R-N : r < vertical bar x vertical bar < r + 1}, N >= 2, N not equal 3, r >0, lambda > 0, Delta(N)u = div(vertical bar del u vertical bar(N-2)del u) is the N-Laplacian operator and f is a continuous function with exponential critical growth.

Multiplicity of data in trial reports and the reliability of meta-analyses: empirical study

Objectives To examine the extent of multiplicity of data in trial reports and to assess the impact of multiplicity on meta-analysis results. Design Empirical study on a cohort of Cochrane systematic reviews. Data sources All Cochrane systematic reviews published from issue 3 in 2006 to issue 2 in 2007 that presented a result as a standardised mean difference (SMD). We retrieved trial reports contributing to the first SMD result in each review, and downloaded review protocols. We used these SMDs to identify a specific outcome for each meta-analysis from its protocol. Review methods Reviews were eligible if SMD results were based on two to ten randomised trials and if protocols described the outcome. We excluded reviews if they only presented results of subgroup analyses. Based on review protocols and index outcomes, two observers independently extracted the data necessary to calculate SMDs from the original trial reports for any intervention group, time point, or outcome measure compatible with the protocol. From the extracted data, we used Monte Carlo simulations to calculate all possible SMDs for every meta-analysis. Results We identified 19 eligible meta-analyses (including 83 trials). Published review protocols often lacked information about which data to choose. Twenty-four (29%) trials reported data for multiple intervention groups, 30 (36%) reported data for multiple time points, and 29 (35%) reported the index outcome measured on multiple scales. In 18 meta-analyses, we found multiplicity of data in at least one trial report; the median difference between the smallest and largest SMD results within a meta-analysis was 0.40 standard deviation units (range 0.04 to 0.91). Conclusions Multiplicity of data can affect the findings of systematic reviews and meta-analyses. To reduce the risk of bias, reviews and meta-analyses should comply with prespecified protocols that clearly identify time points, intervention groups, and scales of interest.

O conto - Subversão e hibridismo na estrutura tradicional

The questioning of fictional identities is central in both texts. Their structure illustrates the Bakhtinian notions of heteroglossia and dialogism and one of their main themes is the structuring and restructuring of social and personal history. Together with the use of irony and humour, the parody of social context, the use of intertextuality and metafiction, the exploration of fragment and of discontinuity, the development of self reflection and the interrogation of the author before the condition of his work, the focusing on the presence of a reader lost in the interpretation of the text, this problematisation of fictional identities places these two novels between the acts of modernism and postmodernism.

Mutating Identities: Clarice Lispector's um sopro de vida - pulsações and Virginia Woolf's between the acts

The questioning of fictional identities is central in both texts. Their structure illustrates the Bakhtinian notions of heteroglossia and dialogism and one of their main themes is the structuring and restructuring of social and personal history. Together with the use of irony and humour, the parody of social context, the use of intertextuality and metafiction, the exploration of fragment and of discontinuity, the development of self reflection and the interrogation of the author before the condition of his work, the focusing on the presence of a reader lost in the interpretation of the text, this problematisation of fictional identities places these two novels between the acts of modernism and postmodernism.

A vária máscara de Joana : melancolia em perto do coração selvagem

Entitled Joana s several mask: the melancholy in Perto do coração selvagem, the work is divided in six parts: the first one consists of the elaboration of a theoretical sketch about the melancholy that it offers the presuppositions that orientate the work, it is a short introduction about the study of the melancholy, a report until our time, the against-depressive ones and the arrival of the melancholy in Brazil and their particularities; the second part raises the theme of the melancholy, deepening its conception until what is called creative melancholy spread by Walter Benjamin, it serves as anchor for Clarice s writing and as a potential force for the processes lived by the characters of this writer; the third part examines Clarice Lispector s method emphasizing important points of production related to the theme of the melancholy, her style is the psychological analysis; the last one parts (fourth, fifth and sixth parts) are divided in topics that illustrate the conflicts, in most of the time contradictory, of the protagonist Joana, as well as, her difficult interaction with the things and the people that surround her. The fragmentary writing, the being's essential searches, the proximity with the death, the multiplicity of voices of feminine, De profundis, surrealist images, the incessant search for the thing , trips, epiphany, the flaw in the language, the taste of the badly, everything starting from melancholy - transformation and creation tool. The work about melancholy (Freud, Benjamin, Kristeva), it s place of ambiguous and contradictory movements. It is a trip that leads to several corporal and psychological sensations of Joana, enigma-scenes to be deciphered and conflicting images that make you wake up for a critical vision of the modern society. Since the beginning, something pulses without stopping, an incessant memory and the search for something that is lost. We are before recyclings of the interior/exterior, pain/pleasure, visions, abyss, ecstasy in the future and an exit through the melancholic light