Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

Solvability of singular second order m-point boundary value problems of Dirichlet type

Let f : [0, 1] x R2 -> R be a function satisfying the Caxatheodory conditions and t(1 - t)e(t) epsilon L-1 (0, 1). Let a(i) epsilon R and xi(i) (0, 1) for i = 1,..., m - 2 where 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1 - In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem [GRAPHICS] The proof of our main result is based on the Leray-Schauder continuation theorem.

Analytical solutions of linear finite- and small-strain one-dimensional consolidation

Analytical solutions are presented for linear finite-strain one-dimensional consolidation of initially unconsolidated soil layers with surcharge loading for both one- and two-way drainage. These solutions complement earlier solutions for initially unconsolidated soil layers without surcharge and initially normally consolidated soil layers with surcharge. Small-strain solutions for the consolidation of initially unconsolidated soil layers with surcharge loading are also presented, and the relationship between the earlier solutions for initially unconsolidated soil without surcharge and the corresponding small-strain solutions, which was not addressed in the earlier work, is clarified. The new solutions for initially unconsolidated soil with surcharge loading can be applied to the analysis of low stress consolidation tests and to the partial validation of numerical solutions of non-linear finite-strain consolidation. They also clarify a formerly perplexing aspect of finite-strain solution charts first noted in numerical solutions. Copyright (C) 2004 John Wiley Sons, Ltd.

Asymptotic bifurcation results for quasilinear elliptic operators

We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

On multiple solutions of the exterior neumann problem involving critical sobolev exponent

In this paper we consider the exterior Neumann problem involving a critical Sobolev exponent. We establish the existence of two solutions having a prescribed limit at infinity.

Relations between coping and positive and negative outcomes in carers of persons with multiple sclerosis (MS)

This study examined relations between stress and coping predictors and negative and positive outcomes in MS caregiving. A total of 222 carers and their care-recipients completed questionnaires at Time 1 and three months later, Time 2 ( n = 155). Predictors included care-recipient characteristics ( age, time since diagnosis, course and life satisfaction), and Times 1 and 2 carer problems, stress appraisal and coping. Dependent variables were Time 2 negative ( anxiety, depression) and positive outcomes ( life satisfaction, positive affect, benefits). Regressions indicated that, overall, the hypothesised direct effects of stress appraisal and coping strategies on positive and negative outcomes were supported. The hypothesised stress-buffering effects of positive reframing coping were also supported. All but one of the coping strategies were related to both positive and negative outcomes; specifically, practical assistance coping emerged as a unique predictor of distress. Of the model predictors, care-recipient life satisfaction emerged as the strongest and most consistent predictor of both positive and negative outcomes except benefit finding. Findings support the role of care-recipient characteristics and the carer's appraisal and coping processes in shaping both positive and negative outcomes. The guiding framework and findings have the potential to inform interventions designed to promote well-being in carers.

Dissolution of porcine incisor pulps in sodium hypochlorite solutions of varying compositions and concentrations

Background: The solubility of dental pulp tissue in sodium hypochlorite has been extensively investigated but results have been inconsistent; due most likely to variations in experimental design, the volume and/or rate of replenishment of the solutions used and the nature of the tissues assessed. Traditionally, the sodium hypochlorite solutions used for endodontic irrigation in Australia have been either Milton or commercial bleach, with Milton being the most common. Recently, a range of Therapeutic Goods Administration (TGA) approved proprietary sodium hypochlorite solutions, which contain surfactant, has become available. Some domestic chlorine bleaches now also contain surfactants. The purpose of this study was to perform new solubility assessments, comparing Milton with new TGA approved products, Hypochlor 1% and Hypochlor 4% forte, and with a domestic bleach containing surfactant (White King). Methods: Ten randomly assigned pulp samples of porcine dental pulp of approximately equal dimensions were immersed in the above solutions, as well as representative concentrations of sodium hydroxide. Time to complete dissolution was measured and assessed statistically. Results: White King 4% showed the shortest dissolution time, closely followed by Hypochlor 4% forte. White King 1% and Hypochlor 1% each took around three times as long to completely dissolve the samples of pulp as their respective 4% concentrations, while Milton took nearly 10 times as long. The sodium hydroxide solutions showed no noticeable dissolution of the pulp samples. Conclusions: The composition and content of sodium hypochlorite solutions had a profound effect on the ability of these solutions to dissolve pulp tissue in vitro. Greater concentrations provided more rapid dissolution of tissue. One per cent solutions with added surfactant and which contained higher concentrations of sodium hydroxide were significantly more effective in dissolution of pulp tissue than Milton.