We investigate a generalization of the equation curlw→=g→ to an arbitrary number n dimensions, which is based on well-known Moisil–Teodorescu differential operator. Explicit solutions are derived for particular problem in bounded domains Rn using classical operators from Clifford analysis. In physically significant case n=3, two explicit div-curl system exterior R3 obtained following different ...

in this paper, a numerical method is developed for solving a linear sixth order boundaryvalue problem (6vbp ) by using the hyperbolic uniform spline of order 3 (lower order). thereis proved to be first-order convergent. numerical results confirm the order of convergencepredicted by the analysis.

In this paper, we investigate the problem of existence and asymptotic behavior of the solutions for the nonlinear boundary value problem ǫy + ky = f(t, y), t ∈ 〈a, b〉, k > 0, 0 < ǫ << 1 satisfying Neumann boundary conditions and where critical manifold is not normally hyperbolic. Our analysis relies on the method upper and lower solutions.

We consider the Neumann boundary value problem for harmonic maps in an annular domain with a large number of small holes. On the boundary of the domain the degree condition is prescribed. We obtain an effective (homogenized) anisotropic nonlinear problem. We also discuss applications of these results to homogenized description of superconducting composites and superfluidity.