Kind Of Boundary Value Problem Research Articles

Quadratic forms, weighted eigenfunctions and boundary value problems for non-linear second order ordinary differential equations

SynopsisSome known results for different kinds of boundary value problems for second order ordinary differential equations are generalised. Different approaches are compared with one another, using topological and variational methods and the theory of weighted eigenvalue problems.

A Rigorous Theory for Problems of Scattering: The Delta Boundary Operator Method

Abstract A rigorous approach for solving a large class of scattering problems is presented and implemented for the classical problem of scattering by a perfectly conducting circular cylinder. This method is characterized by the preliminary calculations of a ψ distribution, deduced from a new kind of boundary value problem. This ψ distribution allows us to express the surface current density in the form of the integral of a known function, valid for any kind of incident wave. Numerical comparisons with the classical method are performed. A numerical study of ψ allows us to deal with cylinders having diameters larger than 100 wavelengths on a HP 1000 F minicomputer.

Proper solutions and limit boundary value problems of nonlinear second-order systems of differential equations

For the system of differential equations (fx1113-1) where a(t) > 0, r(t) > 0 for t ≥ t0; f(x) > 0 and is decreasing for x > 0, g(y) > 0, we give necessary and sufficient condition of the existence of a proper solution, a bounded proper solution or solutions of two kinds of boundary value problems on an infinite interval [c, ∞) c ≥ t0. Several examples are given to illustrate the conditions of these results.

Boundary value problems for minimal surfaces with singularities at infinity

(1. 1) (1 + 2)oxx 2oxy4xy + (1 + ox)lo = 0. In this paper we deal with another kind of boundary value problem for the same equation. We are looking for a solution defined in a domain exterior to a simple closed curve P, possessing at the point at infinity a singularity, having on TP continuous partial derivatives, and satisfying either of the homogeneous boundary conditions (1.2) W: a4/9n = 0, 3: 4 = 0 on 'P. We shall not require, in general, that 45(x, y) be single-valued, but shall assume that (1.3) w = oxic/ is. We shall also prescribe the value of (1.4) qmax = max I w|. It will be convenient to associate with every solution of (1.1) the function (2)