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 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 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.     

Discrete conjugate boundary value problems

This paper discusses higher-order discrete conjugate boundary value problems of singular and nonsingular type.     

On boundary value problem with singular inhomogeneity concentrated on the boundary

We study the asymptotic behavior of solutions to a boundary value problem for the Poisson equation with a singular right-hand side, singular potential and with alternating type of the boundary condition. Assuming that the boundary microstructure is periodic, we construct the limit problem and prove the homogenization theorem by means of the unfolding method. The proof requires that the dimension be larger than two.     

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 classical Nicoletti boundary value problem

We shall derive existence, uniqueness and comparison results for the functional differential equationx(t)=f(t, x), a. e.tI, with classical Nicoletti boundary conditionsx _i(t_i)=y _iX, iA, whereI is a real interval,A is a nonempty set andX is a Banach space.     

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 the discrete boundary value problem for anisotropic equation

In this paper we consider the discrete anisotropic boundary value problem using critical point theory. Firstly we apply the direct method of the calculus of variations and the mountain pass technique in order to reach the existence of at least one nontrivial solution. Secondly we derive some version of a discrete three critical point theorem which we apply in order to get the existence of at least two nontrivial solutions.     

Coexistence of positive solutions of nonlinear three-point boundary value and its conjugate problem

In this paper, the three-point boundary value problem

     

On four-point boundary value problem without growth conditions

We prove the existence of solutions of four-point boundary value problems under the assumption that f fulfils various combinations of sign conditions and no growth restrictions are imposed on f. In contrast to earlier works all our results are proved for the Carathéodory case.