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.

Positive solutions for a fourth order equation with nonlinear boundary conditions

Existence of positive solutions for a fourth order equation with nonlinear boundary conditions, which models deformations of beams on elastic supports, is considered using fixed points theorems in cones of ordered Banach spaces. Iterative and numerical solutions are also considered. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.

Positive solutions for the p-Laplacian involving critical and supercritical nonlinearities with zeros

In this paper we show the existence of multiple solutions to a class of quasilinear elliptic equations when the continuous non-linearity has a positive zero and it satisfies a p-linear condition only at zero. In particular, our approach allows us to consider superlinear, critical and supercritical nonlinearities. (C) 2009 Elsevier Masson SAS. All rights reserved.

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.

Monotone positive solutions for a fourth order equation with nonlinear boundary conditions

This work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions. The results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions. Numerical simulations are also presented. (C) 2009 Elsevier Ltd. All rights reserved.

SOLITON SOLUTIONS TO SYSTEMS OF COUPLED SCHRODINGER EQUATIONS OF HAMILTONIAN TYPE

We study the existence of positive solutions of Hamiltonian-type systems of second-order elliptic PDE in the whole space. The systems depend on a small parameter and involve a potential having a global well structure. We use dual variational methods, a mountain-pass type approach and Fourier analysis to prove positive solutions exist for sufficiently small values of the parameter.

Soliton solutions for quasilinear Schrodinger equations with critical growth

In this paper we establish the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one. whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. (C) 2009 Elsevier Inc. All rights reserved.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Comparative Analysis of the Performance of Various Crystalloid Cardioplegic Solutions on Myocardial Protection After Prolonged Cold Ischemia

Introduction. The quality and effectiveness of myocardial protection are fundamental problems to expand the use of and consequently good outcomes of donated hearts for transplantation. Objective. The purpose of this investigation was to compare the cardioprotective effects of Krebs-Henseleit, Bretschneider-HTK, St Thomas, and Celsior solutions using a modified nonrecirculating Langendorff column model of isolated perfused rat heart during prolonged cold storage. Materials and Methods. After removal 36 rat hearts underwent isolated perfusion into a Langendorff apparatus using Krebs-Henseleit solution for a 15-minute period of recovery; we excluded organs that did not maintain an aortic pressure above 100 m Hg. Subsequently, we equally distributed the hearts into four groups according to the cardioprotection solution; group 1, Krebs-Henseleit (control); group II, Bretschneider-HTK; group III, St Thomas; and group IV, Celsior. Each heart received the specific cardioplegic solution at 10 C for 2-hour storage at 20 C, before a 15 minutes perfusion with Krebs-Henseleit solution for recovery and stabilization. After 60 additional minutes of perfusion, every 5 minutes we determined heart rate (HR), coronary flow (CF), left ventricular systolic pressure (LVSP), and positive and negative peak of the first derivative of left ventricular pressure (+dP/dt and dP/dt, respectively). Results. Comparative analysis by Turkey`s test showed the following performances among the groups at 60 minutes of reperfusion: HR: II = IV > III > I; CF: II = IV > I = III; LVSP: IV > I = II = III; +dP/dt: IV > I = II = III; and dP/dt: IV = II > I = II. Conclusion. Cardioprotective solutions generally used in clinical practice are not able to avoid hemodynamic alterations in hearts exposed to prolonged ischemia. Celsior solution showed better performance than Bretschneider-HTK, St Thomas, and Krebs-Henseleit.

Stability and interface properties of thin cellulose ester films adsorbed from acetone and ethyl acetate solutions

Stability and interface properties of cellulose acetate propionate (CAP) and cellulose acetate butyrate (CAB) films adsorbed from acetone or ethyl acetate onto Si wafers have been investigated by means of contact angle measurements and atomic force microscopy (AFM). Surface energy (gamma(total)(S)) values determined for CAP adsorbed from acetone are larger than those from ethyl acetate. In the case of CAB films adsorbed from ethyl acetate and acetone were similar. Dewetting was observed by AFM only for CAP films prepared from ethyl acetate. Positive values of effective Hamaker constant (A(eff)) were found only for CAP prepared from ethyl acetate, corroborating with dewetting phenomena observed by AFM. Oil the contrary, negative values of A(eff) were determined for CAP and CAB prepared from acetone and for CAB prepared from ethyl acetate, Corroborating with experimental observations. Sum frequency generation (SFG) vibrational spectra indicated that CAP and CAB films prepared from ethyl acetate present more alkyl groups oriented perpendicularly to the polymer-air interface than those films prepared from acetone. Such preferential orientation corroborates with macroscopic contact angle measurements. Moreover, SFG spectra showed that acetone hinds strongly to Si wafers, creating a new surface for CAP and CAB films. (C) 2008 Elsevier Inc. All rights reserved.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Comparison of physical and mechanical properties of microwave-polymerized acrylic resin after disinfection in sodium hypochlorite solutions

This study evaluated the color stability, surface roughness and flexural strength of a microwave-polymerized acrylic resin after immersion in sodium hypochlorite (NaOCl), simulating 20 min of disinfection daily during 180 days. Forty disk-shaped (15 x 4 mm) and 40 rectangular (65 x 10 x 3 mm) specimens were prepared with a microwave-polymerized acrylic resin (Onda-Cryl). Specimens were immersed in either 0.5% NaOCl, 1% NaOCl, Clorox/Calgon and distilled water (control). Color measurements were determined by a portable colorimeter. Three parallel lines, separated by 1.0 mm, were registered on each specimen before and after immersion procedures to analyze the surface roughness. The flexural strength was measured using a 3-point bending test in a universal testing machine with a 50 kgf load cell and a crosshead speed of 1 mm/min. Data were analyzed statistically by ANOVA and Tukey's test (?=0.05). There was no statistically significant differences (p>0.05) among the solutions for color, surface roughness and flexural strength. It may be concluded that immersion in NaOCl solutions simulating short-term daily use during 180 days did not influence the color stability, surface roughness and flexural strength of a microwave-polymerized acrylic resin.

Effect of fluoride-containing solutions on the surface of cast commercially pure titanium

This study evaluated the effects of fluoride-containing solutions on the surface of commercially pure titanium (CP Ti) obtained by casting. CP Ti specimens were fabricated and randomly assigned to 5 groups (n=10): group 1: stored in distilled water at 37 ± 1ºC; group 2: stored in distilled water at 37 ± 1ºC and daily immersed in 0.05% NaF for 3 min; group 3: stored in distilled water at 37 ± 1ºC and daily immersed in 0.2% NaF for 3 min; group 4: stored in distilled water at 37 ± 1ºC; and immersed in 0.05% NaF every 15 days for 3 min; and group 5: stored in distilled water at 37 ± 1ºC and immersed in 0.2% NaF every 15 days for 3 min. Surface roughness was measured with a profilometer immediately after metallographic polishing of the specimens (T0) and at 15-day intervals until completing 60 days of experiment (T15, T30, T45, T60). Data were analyzed statistically by ANOVA and Tukey's test (α=0.05). There was no statistically significant difference (p>0.05) in surface roughness among the solutions. In conclusion, fluoride-containing solutions (pH 7.0) used as mouthwashes do not damage the surface of cast CP Ti and can be used by patients with titanium-based restorations.

Effect of staining solutions and repolishing on color stability of direct composites

OBJECTIVES: The purpose of this study was to assess the color change of three types of composite resins exposed to coffee and cola drink, and the effect of repolishing on the color stability of these composites after staining. MATERIALS AND METHODS: Fifteen specimens (15 mm diameter and 2 mm thick) were fabricated from microhybrid (Esthet-X; Dentsply and Filtek Z-250; 3M ESPE) and high-density hybrid (Surefil; Dentsply) composites, and were finished and polished with aluminum oxide discs (Sof-Lex; 3M ESPE). Color of the specimens was measured according to the CIE L*a*b* system in a refection spectrophotometer (PCB 6807; BYK Gardner). After baseline color measurements, 5 specimens of each resin were immersed in different staining solutions for 15 days: G1 - distilled water (control), G2 - coffee, G3 - cola soft drink. Afterwards, new color measurement was performed and the specimens were repolished and submitted to new color reading. Color stability was determined by the difference (ΔE) between the coordinates L*, a*, and b* obtained from the specimens before and after immersion into the solutions and after repolishing. RESULTS: There was no statistically signifcant difference (ANOVA, Tukey's test; p>0.05) among the ΔE values for the different types of composites after staining or repolishing. For all composite resins, coffee promoted more color change (ΔE>3.3) than distilled water and the cola soft drink. After repolishing, the ΔE values of the specimens immersed in coffee decreased to clinically acceptable values (ΔE<3.3), but remained signifcantly higher than those of the other groups. CONCLUSIONS: No signifcant difference was found among composite resins or between color values before and after repolishing of specimens immersed in distilled water and cola. Immersing specimens in coffee caused greater color change in all types of composite resins tested in this study and repolishing contributed to decrease staining to clinically acceptable ΔE values.

Adhesion of Epiphany and AH Plus sealers to human root dentin treated with different solutions

This study evaluated comparatively the adhesion of Epiphany and AH Plus endodontic sealers to human root dentin treated with 1% NaOCl and 1% NaOCl+17% EDTA, using the push-out test. Sixty root cylinders obtained from maxillary canines had the canals prepared and were randomly assigned to 3 groups (n=20), according to root dentin treatment: GI - distilled water (control), GII - 1% NaOCl and GIII - 1% NaOCl+17% EDTA. Each group was divided into 2 subgroups (n=10) filled with either Epiphany or AH Plus. Bond strength push-out test data (kN) were obtained and analyzed statistically by ANOVA and Tukey's post-hoc test. There was statistically significant difference between sealers (AH Plus: 0.78 ± 0.13; Epiphany: 0.61 ± 0.19; p<0.01) and among root dentin treatments (distilled water: 0.58 ± 0.19; 1% NaOCl: 0.71 ± 0.12; 1% NaOCl+17% EDTA: 0.80 ± 0.17; p<0.05). In conclusion, AH Plus sealer presented greater adhesion to dentin than Epiphany, regardless of the treatment of root canal walls.