On a boundary value problem with integral boundary conditions

We study the existence of positive solutions of second-order ordinary differential equations with integral boundary conditions. The result generalizes the conditions obtained in [1] for the existence of positive solutions.     

On a multi-point discrete boundary value problem

We study the existence and non-existence of positive solutions for a system of nonlinear second-order difference equations subject to multi-point boundary conditions. The proof of the existence of positive solutions is based upon the Schauder fixed point theorem.     

On a double boundary layer in a nonlinear boundary value problem

The question of the isotopy of a quasiconformal mapping and its special aspects in dimension greater than 2 are considered. It is shown that an arbitrary quasiconformal mapping of a ball has an isotopy to the identity map such that the coefficient of quasiconformality (dilatation) of the mapping varies continuously and monotonically. In contrast to the planar case, in dimension higher than 2 such an isotopy is not possible in an arbitrary domain. Examples showing specific features of the multidimensional case are given. In particular, they show that even when such an isotopy exists, it is not always possible to perform an isotopy so that the coefficient of quasiconformality approaches 1 monotonically at each point in the source domain.     

On a boundary value problem in the half-space

In this paper, we study the existence of positive solutions and sign-changing solutions for the following boundary value problem in the half-space

     

On the Sturm-Liouville-type boundary value problem

The problems of existence, uniqueness and continuous dependence on parameter of solutions of the nonlinear boundary value problem of Sturm-Liouville type for ordinary differential equations are considered. The well-known Banach fixed point theorem is used to establish results.     

On the conjugate boundary value problem

We study the conjugate boundary-value problem with boundary conditions whose orders can be as large as the order of the differential equation or larger. We construct the Green's function of the problem over the entire space when the separating surface is a hyperplane, and we describe its properties. Bibliography: 6 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 20–24.     

On the discrete spectrum of a boundary value problem

Odessa. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 182–186, September–October, 1990.     

On a third-order multi-point boundary value problem at resonance

In this paper, we prove some existence results for a third order multi-point boundary value problem at resonance. Our method is based upon the coincidence degree theory of Mawhin.     

On a first-order semipositone discrete fractional boundary value problem

In this paper we demonstrate the existence of at least one positive solution to a discrete fractional semipositone boundary value problem. Our results extend existing results not only due to the fact that the problem we treat here is of fractional order but also due to the fact that the boundary condition we study is potentially very general being as it can be both nonlocal and nonlinear.     

On a nonlinear boundary value problem modeling corneal shape

In this paper we present some results concerning a boundary value problem for a nonlinear ordinary differential equation that was used before in modeling the topography of human cornea. These results generalize previously obtained theorems on existence and uniqueness. We show that our equation has a unique solution for all parameters and conditions that can arise in physical situation. In the second part of the article we derive some new estimates and approximate solutions. Numerical calculations verify that these approximations are very accurate.