# Adjoint and self-adjoint boundary value problems on a geometric graph

## Related Articles

- Dynamics of a second-order nonlinear equation with a large coefficient of delay control. Kashchenko, S. // Doklady Mathematics;Aug2014, Vol. 90 Issue 1, p503
The article discusses the dynamics of a non-linear second order equation having a large coefficient of delay control. Topics include delay control coefficients, delay coefficient, and asymptotic approximations. Boundary value problem, oscillating functions and mathematical theorems are used to...

- INTEGRAL REPRESENTATION OF SOLUTIONS TO BOUNDARY-VALUE PROBLEMS ON THE HALF-LINE FOR LINEAR ODES WITH SINGULARITY OF THE FIRST KIND. HORISHNA, YULIA; PARASYUK, IGOR; PROTSAK, LYUDMYLA // Electronic Journal of Differential Equations;2008, Vol. 2008, Special section p1
We study the existence of solutions to a non-homogeneous system of linear ODEs which has the pole of first order at x = 0; these solutions should vanish at infinity and be continuously differentiable on [0, âˆž). The resonant case where the corresponding homogeneous problem has nontrivial...

- A Necessary and Sufficient Condition for a Linear Differential System to be Strongly Monotone. Andersen, Kurt Munk; Sandqvist, Allan // Bulletin of the London Mathematical Society;1998, Vol. 30 Issue 6, p585
In order to present the results of this note, we begin with some definitions. Consider a differential system[formula]where IâŠ†R is an open interval, and f(t, x), (t, x)âˆˆIÃ—Rn, is a continuous vector function with continuous first derivatives Î´fr/Î´xs, r, s=1, 2, â€¦, n.Let...

- Î¨ -- BOUNDED SOLUTIONS FOR A LYAPUNOV MATRIX DIFFERENTIAL EQUATION. Diamandescu, Aurel // Electronic Journal of Qualitative Theory of Differential Equatio;Mar2009, Special section p1
It is proved a necessary and sufficient condition for the existence of at least one Ïˆ- bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation.

- A general test for the reducibility of linear differential systems and properties of the reducibility coefficient. Izobov, N. A.; Mazanik, S. A. // Differential Equations;Feb2007, Vol. 43 Issue 2, p196
The article studies the Reducibility of linear differential systems and properties of the Reducibility Coefficient. The article considers linear differential systems with piecewise continuous bounded coefficient matrices and perturbed systems with perturbations and piecewise continuous on the...

- On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations. Rontó, A.; Rontó, M. // Abstract & Applied Analysis;2011, Special section p1
For a system of linear functional differential equations, we consider a three-point problem with nonseparated boundary conditions determined by singular matrices. We show that, to investigate such a problem, it is often useful to reduce it to a parametric family of two-point boundary value...

- Vibration Analysis of a Variable Thickness Isotropic Kirchhoff Annular Plate Covered with Piezoelectric Layers Using Modified Wave Method. Saleh, N. Rasekh; Bahrami, M. N.; Novin, M. H. Kargar // Journal of Applied Sciences Research;Aug2011, Vol. 7 Issue 8, p1172
In this paper, based on Kirchhoff plate theory (CLPT), vibration analysis of an arbitrary nonlinear variable thickness annular isotropic plate which is covered with piezoelectric layers on the top and bottom surfaces in a short circuit state is performed using a semi-analytic method, named...

- Modified Block SSOR Preconditioners for Symmetric Positive Definite Linear Systems. Zhong-Zhi Bai // Annals of Operations Research;2001, Vol. 103 Issue 1-4, p263
A class of modified block SSOR preconditioners is presented for the symmetric positive definite systems of linear equations, whose coefficient matrices come from the hierarchical-basis finite-element discretizations of the second-order self-adjoint elliptic boundary value problems. These...

- On Boundary Value Problems for Linear Differential Systems with Singularities. Kiguradze, I. T. // Differential Equations;Feb2003, Vol. 39 Issue 2, p212
Examines the boundary value problems for linear differential systems with singularities. Statement of problem and basic notation; Fredholm property of the problems; Conditions under which the problem of finding a solution of the linear differential system is considered.