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 paper, we consider a class of boundary value problems of fractional differential equations with integral and anti-periodic boundary conditions, which is a new type of mixed boundary condition. By using the contraction mapping principle, Krasnosel’skii fixed point theorem, and Leray-Schauder degree theory, we obtain some results of existence and uniqueness. Finally, several examples are ...

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...

In the first part of this chapter we focus on the question of well-posedness of boundary-value problems for linear partial differential equations of elliptic type. The second part is devoted to the construction and the error analysis of finite difference schemes for these problems. It will be assumed throughout that the coefficients in the equation, the boundary data and the resulting solution ...

Selfdual variational theory – developed in [7] and [8] – allows for the superposition of appropriate boundary Lagrangians with “interior” Lagrangians, leading to a variational formulation and resolution of problems with various linear and nonlinear boundary constraints that are not amenable to standard Euler-Lagrange theory. The superposition of several selfdual Lagrangians is also possible in ...