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...

In this paper, we present some new fixed point theorems for both single-valued and multi-valued maps controlled by the contraction conditions with perturbed linear operators in continuous function spaces. Our results can be applied to various integral operators. Some previous results are generalized in this literature. As applications, the existence and uniqueness of solutions of impulsive peri...

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. §

It is shown that the non-homogeneous Dirichlet and Neuman problems for the 2-order Seiberg-Witten equation admit a regular solution once the H-condition 3.1.1 is satisfied. The approach consist in applying the elliptic techniques to the variational setting of the Seiberg-Witten equation.

In this chapter we discuss discrete variable methods for solving BVPs for ordinary differential equations. These methods produce solutions that are defined on a set of discrete points. Methods of this type are initial-value techniques, i.e., shooting and superposition, and finite difference schemes. We will discuss initialvalue and finite difference methods for linear and nonlinear BVPs, and th...