Artūras Štikonas

Investigation of Characteristic Curve for Sturm–Liouville Problem with Nonlocal Boundary Conditions on Torus

In this paper, we investigate the second-order Sturm–Liouville problem with two additional Nonlocal Boundary Conditions. Nonlocal boundary conditions depends on two parameters. We find condition for existence of zero eigenvalue in the parameters space and classified Characteristic Curves in the plane and extended plane is described as torus. The Characteristic Curve on torus may be of three types only. Some new conclusions about existence and uniqueness domain of solution are presented.

Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions

We investigate a second-order discrete problem with two additional conditions which are described by a pair of linearly independent linear functionals. We have found the solution to this problem and presented a formula and the existence condition of Greens function if the general solution of a homogeneous equation is known. We have obtained the relation between two Greens functions of two nonhomogeneous problems. It allows us to find Greens function for the same equation but with different additional conditions. The obtained results are applied to problems with nonlocal boundary conditions.

Spectrum Curves for Sturm–Liouville Problem with Integral Boundary Condition

We consider Sturm–Liouville problem with one integral type nonlocal boundary condition depending on three parameters γ (multiplier in nonlocal condition), ξ1, ξ2 ([ξ1, ξ2] is a domain of integration). The distribution of zeroes, poles, and constant eigenvalue points of Complex Characteristic Function is presented. We investigate how Spectrum Curves depend on the parameters of nonlocal boundary conditions. In this paper we describe the behaviour of Spectrum Curves and classify critical points of Complex-Real Characteristic function. Phase Trajectories of critical points in Phase Space of the parameters ξ1, ξ2 are investigated. We present the results of modelling and computational analysis and illustrate those results with graphs.

Green’s Matrices for First Order Differential Systems with Nonlocal Conditions∗

In this paper, we investigate the linear system of first order ordinary differential equations with nonlocal conditions. Green’s matrices, their explicit representations and properties are considered as well. We present the relation between the Green’s matrix for the system and the Green’s function for the differential equation. Several examples are also given.

The minimum norm least squares solution to the discrete nonlocal problems

In this paper, we introduce two finite Hilbert spaces instead of standard Euclidean space and consider the generalized minimum norm least squares solution to the second order discrete problem. Applying obtained properties, we investigate the convergence of this discrete solution to a solution of the differential problem.

On the Stability of a Weighted Finite Difference Scheme for Hyperbolic Equation with Integral Boundary Conditions

We consider second order hyperbolic equation with nonlocal integral boundary conditions. We study the spectrum of the weighted difference operator for the formulated problem. Using the characteristic function we investigate the spectrum of the transition matrix of the three-layered finite difference scheme and obtain spectral stability conditions subject to boundary parameters γ0, γ1 and piecewise constant weight functions.

Some estimates for a special linear difference parabolic equation

Abstract The finite‐difference scheme for a special linear parabolic equation is investigated. A priori estimates for such finite‐difference scheme are derived in the difference analogues of norm on Banach function spaces V2 and W 2 2,1.