Investigation of matrix nullity for the second order discrete nonlocal boundary value problem

Positive Solutions to a Second-Order Discrete Boundary Value Problem

Boundary Value Problem for Second-order Differential Operators with Mixed Nonlocal Boundary Conditions

In this paper, we study a second order differential operator with mixed nonlocal boundary conditions combined weighting integral boundary condition with another two point boundary condition. Under certain conditions on the weighting functions and on the coefficients in the boundary conditions, called non regular boundary conditions, we prove that the resolvent decreases with respect to the spec...

The Discrete First-Order System Least Squares: The Second-Order Elliptic Boundary Value Problem

In [Z. Cai, T. Manteuffel, and S. F. McCormick, SIAM J. Numer. Anal., 34 (1997), pp. 425–454], an L2-norm version of first-order system least squares (FOSLS) was developed for scalar second-order elliptic partial differential equations. A limitation of this approach is the requirement of sufficient smoothness of the original problem, which is used for the equivalence of spaces between (H1)d and...

Nonlocal Boundary Value Problem for Second Order Abstract Elliptic Differential Equation

We establish conditions that guarantee Fredholm solvability in the Banach space Lp of nonlocal boundary value problems for elliptic abstract differential equations of the second order in an interval. Moreover, in the space L2 we prove in addition the coercive solvability, and the completeness of root functions (eigenfunctions and associated functions). The obtained results are then applied to t...

A Nonlinear Second Order Problem Witha Nonlocal Boundary Condition

We study a nonlinear problem of pendulum-type for a p-Laplacian with nonlinear periodic-type boundary conditions. Using an extension of Mawhin’s continuation theorem for nonlinear operators, we prove the existence of a solution under a LandesmanLazer type condition. Moreover, using the method of upper and lower solutions, we generalize a celebrated result by Castro for the classical pendulum eq...