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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the properness of an impulsive control extension of dynamic optimization problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Anti-erosive properties of solutions containing fluoride and different film-forming agents

Objectives: To evaluate the anti-erosive potential of solutions containing sodium fluoride (NaF, 225 ppm F) and different film-forming agents.Methods: In Phase 1, hydroxyapatite crystals were pre-treated with solutions containing NaF (F), linear sodium polyphosphate (LPP), sodium pyrophosphate tetrabasic (PP), sodium tripolyphosphate (STP), sodium caseinate (SC), bovine serum albumin (BSA), stannous chloride (Sn) and some combinations thereof. Deionized water was the control (C). The pH-stat method was used to evaluate hydroxyapatite dissolution. In Phase 2, the most effective solutions were tested in two independent experiments. Both consisted of an erosion-remineralization cycling model using enamel and dentine specimens with three solution treatments per day. In Phase 2a, the challenge was performed with 0.3% citric acid (pH = 3.8). In Phase 2b, 1% citric acid (pH = 2.4) was used. Hard tissue surface loss was determined profilometrically. Data were analyzed with two-way ANOVA and Tukey tests.Results: In Phase 1, F, LPP, Sn and some of their combinations caused the greatest reduction in hydroxyapatite dissolution. In Phase 2a, C showed the highest enamel loss, followed by LPP. There were no differences between all other groups. In Phase 2b: (F + LPP + Sn) < (F + LPP) = (F + Sn) < (F) = (LPP + Sn) < (LPP) < (Sn) < C. For dentine, in both experiments, only the fluoride-containing groups showed lower surface loss than C, except for LPP + Sn in 2a.Conclusions: F, Sn, LPP reduced enamel erosion, this effect was enhanced by their combination under highly erosive conditions. For dentine, the F-containing groups showed similar protective effect.Clinical significance: The addition of LPP and/or Sn can improve the fluoride solution protection against erosion of enamel but not of dentine. (C) 2015 Elsevier Ltd. All rights reserved.

A generalized Riemann- Stieltjes integral on time scales and discontinuous dynamical equations

This paper is concerned with a generalization of the Riemann- Stieltjes integral on time scales for deal with some aspects of discontinuous dynamic equations in which Riemann-Stieltjes integral does not works. © 2011 Academic Publications.

Modelos descritos por equações diferenciais ordinárias

Pós-graduação em Matemática Universitária - IGCE

Existência de soluções de inclusões diferenciais em escalas temporais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Sobre o teorema do valor intermediário

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Existência de soluções para equações integrodiferenciais em epaços de Banach

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Inclusões Dinâmicas em Escalas Temporais: Existência de Soluções sob a Hipótese de Semicontinuidade Inferior

In this paper we consider the problem of differential inclusion in time scales whose vector field is a multifunction, that is, a function that maps points to sets. It is provided conditions of existence without requiring compactness of the vector field; it is required that the vector field is closed, convex, and lower semicontinuous. In previous work in literature, it is required that the field is either scalar or compact, convex, and has closed graph.

On retarded differential equations with impulses

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Exact closed-form solutions of the Dirac equation for a class of effective Morse potentials

Exact bounded solutions for a fermion subject to exponential scalar potential in 1 + 1 dimensions are found in closed form. We discuss the existence of zero modes which are related to the ultrarelativistic limit of the Dirac equation and are responsible for the induction of a fractional fermion number on the vacuum.

Exact closed-form solutions of the Dirac equation with a scalar exponential potential

The problem of a fermion subject to a general scalar potential in a two-dimensional world for nonzero eigenenergies is mapped into a Sturm-Liouville problem for the upper component of the Dirac spinor. In the specific circumstance of an exponential potential, we have an effective Morse potential which reveals itself as an essentially relativistic problem. Exact bound solutions are found in closed form for this problem. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail, particularly the existence of zero modes. (c) 2005 Elsevier B.v. All rights reserved.

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

Periodic solutions of abstract neutral functional differential equations

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier B.V. All rights reserved.