Some classical tools have been used in the literature to study the positive solutions for twopoint boundary value problems of a coupled system of differential equations. These classical tools include some fixed point theorems in cones for completely continuous operators and Leray-Schauder fixed point theorem; for examples, see 1–3 and literatures therein. Recently, Schauder’s fixed point theore...

By constructing some special cones and using fixed point theorem of cone expansion and compression, this paper presents some necessary and sufficient conditions for the existence of C4n−2 positive solutions to a class of singular boundary-value problems. Some examples are presented to illustrate our main results.

where 1 < α < 2, 0 < βi < 1, i = 1, 2, . . . ,m – 2, 0 < η1 < η2 < · · · < ηm–2 < 1, ∑m–2 i=1 βiη α–1 i < 1, D α 0+ is the standard Riemann–Liouville derivative. Here our nonlinearity f may be singular at u = 0. As an application of Green’s function, we give some multiple positive solutions for singular positone and semipositone boundary value problems by means of the Leray–Schauder nonlinear a...

Using a fixed point theorem in cones, this paper shows the existence of positive solutions for the singular three-point boundary-value problem x′′(t) + a(t)f(t, x(t), x′(t)) = 0, 0 < t < 1, x′(0) = 0, x(1) = αx(η), where 0 < α < 1, 0 < η < 1, and f may change sign and may be singular at x = 0 and x′ = 0.

As a global feature of fingerprints, singular point plays important roles in fingerprint model, synthesis fingerprint, fingerprint classification, fingerprint alignment and so on. In our previous work, a rapid and effective fingerprint singular points detection method was proposed. That method detects singular points based on partitioning the orientation field into a serious non-overlapping hom...

A theorem of Mumford’s states that for a smooth cubic threefold X, the intermediate Jacobian JX is a principally polarized abelian variety of dimension 5 whose theta divisor has a unique singular point, which has multiplicity three. This talk describes joint work with R. Friedman, in which we prove a converse: if A is a principally polarized abelian variety of dimension 5 whose theta divisor ha...

The soft and collinear singularities of general scalar and tensor one-loop N -point integrals are worked out explicitly. As a result a simple explicit formula is given that expresses the singular part in terms of 3-point integrals. Apart from predicting the singularities, this result can be used to transfer singular one-loop integrals from one regularization scheme to another or to subtract sof...

We give a family of augmented systems as well as minimally extended systems which are suitable for the numerical detection and determination of singular points of Banach space problems. The systems are constructed in such a way that they only diier in a small part which must be adapted to the equivalence class to which the desired singular point belongs. The presented general results are specia...

Some of the most common problems in applied sciences and engineering are usually formulated as singular two-point boundary value problems. A well known fact is that the exact solutions in closed form of such problems were not obtained in many cases. In this paper, the exact solutions for a wide class of singular two-point boundary value problems are obtained by using Adomian decomposition method.

Abstract In this paper, we have developed a fifth order compact difference method for a class of singularly perturbed singular two-point boundary value problems. To avoid the singularity at zero a terminal boundary condition in the implicit form is derived. Using this condition as one of the boundary condition we solve the singularly perturbed singular two-point boundary value problem by the fi...