We consider some Boussinesq systems of water wave theory, which are of coupled KdV type. After a brief review of the theory of existence-uniqueness of solutions of the associated initial-value problems, we turn to the numerical solution of their initialand periodic boundary-value problems by unconditionally stable, highly accurate methods that use Galerkin/finite element type schemes with perio...

This article analyzes a nonlinear system of first-order difference equations with periodic and non-periodic boundary conditions. Some sufficient conditions are presented under which: potential solutions to the equations will satisfy certain a priori bounds; and the equations will admit at least one solution. The methods involve new dynamic inequalities and use of Brouwer degree theory. The new ...

In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...

Some classical tools have been used in the literature to study the positive solutions for twopoint boundary value problems of a coupled system of differential equations. These classical tools include some fixed point theorems in cones for completely continuous operators and Leray-Schauder fixed point theorem; for examples, see 1–3 and literatures therein. Recently, Schauder’s fixed point theore...

The theory of the nonlocal linear boundary value problems is still on the level of examples. Any attempt to encompass them by a unified scheme sticks upon the lack of general methods. Here we are to outline an algebraic approach to linear nonlocal boundary value problems. It is based on the notion of convolution of linear operator and on operational calculus on it. Our operators are right inver...

In this work we analyze the boundary value problems on a path associated with Schrödinger operators with constant ground state. These problems include the cases in which the boundary has two, one or none vertices. In addition, we study the periodic boundary value problem that corresponds to the Poisson equation in a cycle. Moreover, we obtain the Green’s function for each regular problem and th...

We consider multivariate sequences, deened by a partial linear recurrence equation together with appropriate boundary conditions. The domain of deenition of these sequences is the rst orthant of the integer lattice, restricted in some dimensions to an initial segment of the nonnegative integers. By means of the kernel method we obtain an explicit expression for the generating function of the so...

Impulsive differential equations, which arise in biology, physics, population dynamics, economics, etc., are a basic tool to study evolution processes that are subjected to abrupt in their states (see [8-12]). Recently, the existence results were extended to anti-periodic boundary value problems for first-order impulsive differential equations [13,14]. Very recently, Wang and Shen [15] investig...

Solutions are obtained for the boundary value problem, y(n) + f(x, y) = 0, y(i)(0) = y(1) = 0, 0 ≤ i ≤ n − 2, where f(x, y) is singular at y = 0. An application is made of a fixed point theorem for operators that are decreasing with respect to a cone. §