In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function α , a nonlinear term f , and a numerical parameter λ : ∆ ( α (k) |∆u(k − 1)|p(k−1)−2∆u(k − 1) ) + λf(k, u(k)) = 0, k ∈ [1, T ] . We derive the intervals of a numerical parameter λ for which the considered BVP has at least 1, exactly 1, or at least 2 positive solutions. Some useful discrete ine...

which arises in many different areas of applied mathematics and physics. Singular problems of this type that the nonlinearity g may change sign are referred to as singular semipositone problems in the literature. Motivated by BVP (1.1), this paper presents the existence results of the following second-order singular semipositone boundary value problem: { u ′′ + f(t, u) + g(t, u) = 0, 0 < t < 1,...

The boundary value problem (BVP) for a class of nonlinear ordinary differential equations is examined. It can be used to describe the eversion problem for a spherical shell composed of a class of transversely isotropic incompressible Mooney-Rivlin materials. The solutions of the nonlinear equation describing the relation among deformed thickness, initial thickness and material parameters of the...

2 School of Mathematics The University of New South Wales, Sydney NSW 2052, Australia Abstract:We consider a boundary value problem (BVP) for systems of second-order dynamic equations on time scales. Using methods involving dynamic inequalities, we formulate conditions under which all solutions to a certain family of systems of dynamic equations satisfy certain a priori bounds. These results ar...

We find a Green’s function for the singular third-order three-point BVP u′′′(t) = −a(t)f(t, u(t)), u(0) = u′(1) = u′′(η) = 0 where 0 ≤ η < 1/2. Then we apply the classical Krasnosel’skii’s fixed point theorem for finding solutions in a cone. Although this problem Green’s function is not positive, the obtained solution is still positive and increasing. Our techniques rely on a combination of a f...

In this paper, we estimate the reliability of a parallel system with two components. We assume that the strengths of these components follow bivariate pareto (BVP) distribution proposed by Veenus and Nair(1994). These two components are subjected to either two independent stresses or common stress which are ( is ) independent of strengths of two components. We assume that the distribution of st...

Abstract Compliant mechanisms (CMs) have presented its inherently advantageous properties due to the fact that CMs utilize elastic deformation of elementary flexible members transfer motion, force, and energy. Previously, classic Euler–Bernoulli beam theory is most used in terms modeling large deflections CMs. However, it has some assumptions may decrease accuracy, such as ignoring shear strain...