Wiener-Hopf type problems for elliptic systems of singular integral equations

On Solutions of a System of Wiener-Hopf Integral Equations

Consider the problem of solving a system of Wiener-Hopf integral equations

An effective method for approximating the solution of singular integral equations with Cauchy kernel type

In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, w...

A Generalization of the Wiener - Hopf Integral

where now N(x) is integrable in any interval which excludes the origin, O(e') as x -i o and O('/x) as x -O 0. The plus sign in the kernel now changes the entire mode of attack. While Fourier transform methods still play a dominant r6le in our work, we cannot solve the equation (1.2) in one fell swoop as we do equation (1.1). Instead we find it necessary to take advantage of the special assumpti...

Singular perturbation problems for nonlinear elliptic equations in degenerate settings

Here N ≥ 1, g(s) ∈ C(R,R) is a function with a subcritical growth, V (x) ∈ C(R ,R) is a positive function and 0 < ε 1. Among solutions of (0.1)ε, we are interested in concentrating families (uε) of solutions, which have the following behavior: (i) uε(x) has a local maximum at xε ∈ R and xε converges to some x0 ∈ R as ε → 0. (ii) rescaled function vε(y) = uε(εy + xε) converges as ε → 0 to a solu...

Asymptotic Solutions of Singular Perturbation Problems for Linear Differential Equations of Elliptic Type