Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Supply chain management as beyond operational efficiency

The orthodoxy of supply chain management (SCM) emphasises competitive advantage through increased operational efficiency and market responsiveness from production and distribution processes into the hands of consumers. It anticipates that future competition will be between chains rather than between firms. While well established in other industry sectors, the SCM concept is newly developed in the Australian agri-food sector. Critical review of the concept has identified key issues of power among channel members, processes of chain initiation and innovation, and the inability of SCM to offer a viable business strategy for some firms. Building on those insights, this paper examines the supply chain concept for horticulture. Horticultural products are characterised by perishability, heterogeneity and lags in production response to market signals. Producers’ profits are vulnerable to quantity, timing of supply and product specification. Many supply chains in smaller industries are loose, fragmented, interwoven, unstable and unique! Firms operating within these environments need an astute understanding of the chains, the hierarchy of channel members and their relative position. Effective business strategies – for individual firms and supply chains - need to be developed and redeveloped to accommodate the dynamic nature of horticulture. Two case studies are discussed as contributions to this early stage of the theoretical development of supply chain management. The SCM concept also has implications for horticultural researchers, involving a wider range of industry stakeholders, technical problems and research skills. As for business management, the usefulness of the concept will depend on its capacity to increase responsiveness to customers’ preferences and customer value.

Men's perceived health needs

Cross-sectional survey data describing health priorities and needs perceived by men and women living in Newcastle, Australia are compared and contrasted with national health policies. The highest prevalence of felt needs for men were stress (13 percent), cost of medical care (10 percent) and money problems (9 percent); while stress (16 percent), overweight (16 percent) and money problems (15 percent) were highest for women. These contrast with the 2000 National Health Priorities of cancer. mental health, injury, cardiovascular health, diabetes and asthma. We conclude that men's perceived unmet health needs are similar to those of women; while sharing some commonalities, they also differ from health professional priorities. Incorporating felt needs into health service planning and delivery is a critical unmet challenge for government planners.

The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Consumers' perceived risk: Sources versus consequences

In this study, we examine an important factor that affects consumers' acceptance of business-to-commerce (B2C) electronic commerce - perceived risk. The objective of this paper is to examine the definition of perceived risk in the context of B2C electronic commerce. The paper highlights the importance of perceived risk and the interwoven relation between perceived risk and trust. It discusses the problem of defining perceived risk in prior B2C research. This study proposes a new classification of consumers' perceived risk based on sources. It highlights the importance of identifying the sources of consumer's risk perceptions in addition to the consequences dimensions. Two focus group discussion sessions were conducted to verify the proposed classification. Results indicate that Internet consumers perceive three sources of risk in B2C electronic commerce: technology, vendor, and product. © 2003 Elsevier B.V. All rights reserved.

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.