Semilinear elliptic problems near resonance with a nonprincipal eigenvalue

We consider the Dirichlet problem for the equation -Delta u = lambda u +/- (x, u) + h(x) in a bounded domain, where f has a sublinear growth and h is an element of L-2. We find suitable conditions on f and It in order to have at least two solutions for X near to an eigenvalue of -Delta. A typical example to which our results apply is when f (x, u) behaves at infinity like a(x)vertical bar u vertical bar(q-2)u, with M > a(x) > delta > 0, and I < q < 2. (C) 2007 Elsevier Inc. All rights reserved.

SUPERLINEAR ELLIPTIC PROBLEMS WITH SIGN CHANGING COEFFICIENTS

Via variational methods, we study multiplicity of solutions for the problem {-Delta u = lambda b(x)vertical bar u vertical bar(q-2)u + au + g(x, u) in Omega, u - 0 on partial derivative Omega, where a simple example for g( x, u) is |u|(p-2)u; here a, lambda are real parameters, 1 < q < 2 < p <= 2* and b(x) is a function in a suitable space L-sigma. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any lambda > 0, and a total of five nontrivial solutions are obtained when lambda is small and a >= lambda(1). Note that this type of results are valid even in the critical case.

Lions-type compactness and Rubik actions on the Heisenberg group

In this paper we prove a Lions-type compactness embedding result for symmetric unbounded domains of the Heisenberg group. The natural group action on the Heisenberg group TeX is provided by the unitary group U(n) × {1} and its appropriate subgroups, which will be used to construct subspaces with specific symmetry and compactness properties in the Folland-Stein’s horizontal Sobolev space TeX. As an application, we study the multiplicity of solutions for a singular subelliptic problem by exploiting a technique of solving the Rubik-cube applied to subgroups of U(n) × {1}. In our approach we employ concentration compactness, group-theoretical arguments, and variational methods.

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zeros

Using a combination of several methods, such as variational methods. the sub and supersolutions method, comparison principles and a priori estimates. we study existence, multiplicity, and the behavior with respect to lambda of positive solutions of p-Laplace equations of the form -Delta(p)u = lambda h(x, u), where the nonlinear term has p-superlinear growth at infinity, is nonnegative, and satisfies h(x, a(x)) = 0 for a suitable positive function a. In order to manage the asymptotic behavior of the solutions we extend a result due to Redheffer and we establish a new Liouville-type theorem for the p-Laplacian operator, where the nonlinearity involved is superlinear, nonnegative, and has positive zeros. (C) 2009 Elsevier Inc. All rights reserved.

Characterization of aqueous silver nitrate solutions for leakage tests

OBJECTIVE: To determine the pH over a period of 168 h and the ionic silver content in various concentrations and post-preparation times of aqueous silver nitrate solutions. Also, the possible effects of these factors on microleakage test in adhesive/resin restorations in primary and permanent teeth were evaluated. MATERIAL AND METHODS: A digital pHmeter was used for measuring the pH of the solutions prepared with three types of water (purified, deionized or distilled) and three brands of silver nitrate salt (Merck, Synth or Cennabras) at 0, 1, 2, 24, 48, 72, 96 and 168 h after preparation, and storage in transparent or dark bottles. Ionic silver was assayed according to the post-preparation times (2, 24, 48, 72, 96, 168 h) and concentrations (1, 5, 25, 50%) of solutions by atomic emission spectrometry. For each sample of each condition, three readings were obtained for calculating the mean value. Class V cavities were prepared with enamel margins on primary and permanent teeth and restored with the adhesive systems OptiBond FL or OptiBond SOLO Plus SE and the composite resin Filtek Z-250. After nail polish coverage, the permanent teeth were immersed in 25% or 50% AgNO3 solution and the primary teeth in 5% or 50% AgNO3 solutions for microleakage evaluation. ANOVA and the Tukey's test were used for data analyses (α=5%). RESULTS: The mean pH of the solutions ranged from neutral to alkaline (7.9±2.2 to 11.8±0.9). Mean ionic silver content differed depending on the concentration of the solution (4.75±0.5 to 293±15.3 ppm). In the microleakage test, significant difference was only observed for the adhesive system factor (p=0.000). CONCLUSIONS: Under the tested experimental conditions and based on the obtained results, it may be concluded that the aqueous AgNO3 solutions: have neutral/alkaline pH and service life of up to 168 h; the level of ionic silver is proportional to the concentration of the solution; even at 5% concentration, the solutions were capable of indicating loss of marginal seal in the composite restorations; the 3-step conventional adhesive system had better performance regarding microleakage in enamel on primary and permanent teeth.

Some (3+1)-dimensional vortex solutions of the CP(N) model

We present a class of solutions of the CP(N) model in (3 + 1) dimensions. We suggest that they represent vortexlike configurations. We also discuss some of their properties. We show that some configurations of vortices have a divergent energy per unit length while for the others such an energy has a minimum for a very special orientation of vortices. We also discuss the Noether charge densities of these vortices.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.

General clas of inhomogeneous perfect-fluid solutions

We present a general class of solutions to Einstein's field equations with two spacelike commuting Killing vectors by assuming the separation of variables of the metric components. The solutions can be interpreted as inhomogeneous cosmological models. We show that the singularity structure of the solutions varies depending on the different particular choices of the parameters and metric functions. There exist solutions with a universal big-bang singularity, solutions with timelike singularities in the Weyl tensor only, solutions with singularities in both the Ricci and the Weyl tensors, and also singularity-free solutions. We prove that the singularity-free solutions have a well-defined cylindrical symmetry and that they are generalizations of other singularity-free solutions obtained recently.

Relaxivity of Gd-based contrast agents on X nuclei with long intrinsic relaxation times in aqueous solutions.

The relaxivity of commercially available gadolinium (Gd)-based contrast agents was studied for X-nuclei resonances with long intrinsic relaxation times ranging from 6 s to several hundred seconds. Omniscan in pure 13C formic acid had a relaxivity of 2.9 mM(-1) s(-1), whereas its relaxivity on glutamate C1 and C5 in aqueous solution was approximately 0.5 mM(-1) s(-1). Both relaxivities allow the preparation of solutions with a predetermined short T1 and suggest that in vitro substantial sensitivity gains in their measurement can be achieved. 6Li has a long intrinsic relaxation time, on the order of several minutes, which was strongly affected by the contrast agents. Relaxivity ranged from approximately 0.1 mM(-1) s(-1) for Omniscan to 0.3 for Magnevist, whereas the relaxivity of Gd-DOTP was at 11 mM(-1) s(-1), which is two orders of magnitude higher. Overall, these experiments suggest that the presence of 0.1- to 10-microM contrast agents should be detectable, provided sufficient sensitivity is available, such as that afforded by hyperpolarization, recently introduced to in vivo imaging.

PHOTOCATALYTIC OXIDATION OF AQUEOUS SOLUTIONS OF JET FUEL AND ICING INHIBITORS

The present paper is devoted to the results of experimental research undertaken into photocatalytical oxidation (PCO) of aqueous solutions of de-icing agents and aqueous extract of jet fuel. The report consists of introduction, literature review, description of materials and methods, discussion of results and conclusions. TiO2 was selected as a photocatalyst for the experiments with synthetic solutions of ethylene glycol, 2-ethoxyethanol and aqueous extract of jet fuel. To explain the PCO mechanisms affecting certain behaviour of de-icing agent under distinctive conditions, the following factors were studied: the impact of initial concentration of pollutant, the role of pH, the presence of tert-butanol as OH·-radicals scavenger and mineral admixtures. PCO under solar radiation performed in two ways: catalysed by irradiated TiO2 slurry or by TiO2 attached to buoyant hollow glass micro-spheres. Special attention was paid to the energy-saving PCO with reduced intensity mixing of the slurry. The effect of PCO was assessed by determination of residual chemical oxygen demand of solution (COD) and by measuring of concentration of glycols. The PCO process efficiency was assumed to be dependent on the TiO2 suspension fractional composition. Thus, the following effects of solutions’ media were viewed: presence of organic admixtures, pH influence, mixing mode during the PCO. The effects of mineral admixtures - Ca2+, Fe3+/2+, Mn2+, SO42- - that are often present in natural and wastewater systems or produced during the degradation of organic pollutants and which can affect the rate of PCO of de-icing agents, were also investigated.

Highly eccentric hip-hop solutions of the 2N

We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ϵ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ϵ ≠ 0, the topological transversality persists and Brouwer's fixed point theorem shows the existence of this kind of solutions in the full system

Growing Up in Exile : An Ethnography of Somali Youth Raised in Kakuma Refugee Camp, Kenya

La violence chronique qui caractérise la Somalie depuis plus de deux décennies a forcé près de deux millions de personnes à fuir. Cette ethnographie étudie l’expérience de l’asile prolongé de jeunes Somaliens qui ont grandi au camp de Kakuma, au Kenya. Leur expérience est hors du commun, bien qu’un nombre croissant de réfugiés passent de longues années dans des camps pourtant conçus comme temporaires, en vertu de la durée des conflits et de la normalisation de pratiques de mise à l’écart de populations « indésirables ». Nous explorons la perception qu’ont ces jeunes de leur environnement et de quelle façon leur exil structure leur perception du passé et de leur pays d’origine, et de leur futur. Ce faisant, nous considérons à la fois les spécificités du contexte et l’environnement global, afin de comprendre comment l’expérience des gens est façonnée par (et façonne) les dynamiques sociales, politiques, économiques et historiques. Nous observons que le camp est, et demeure, un espace de confinement, indépendamment de sa durée d’existence ; bien que conçu comme un lieu de gestion rationnelle des populations, le camp devient un monde social où se développent de nouvelles pratiques ; les jeunes Somaliens font preuve d’agentivité et interprètent leur expérience de manière à rendre leur quotidien acceptable ; ces derniers expriment une frustration croissante lorsque leurs études sont terminées et qu’ils peinent à s’établir en tant qu’adultes, ce qui exacerbe leur désir de quitter le camp. En effet, même s’il existe depuis plus de 20 ans, le camp demeure un lieu de transition. L’expérience de jeunes Somaliens qui ont grandi dans un camp de réfugiés n’a pas été étudiée auparavant. Nous soutenons que cette expérience est caractérisée par des tensions entre contraintes et opportunités, mobilité et immobilité, isolation et connexion ou victimisation et affirmation du sujet – et des temporalités contradictoires. Cette étude souligne que des notions comme la convivialité ou la pluralité des appartenances développées dans la littérature sur la cohabitation interethnique dans les villes ou sur l’identité des migrants aident à appréhender le réalité du camp. Cette ethnographie montre également que, loin d’être des victimes passives, les réfugiés contribuent à trouver des solutions à leur exil.