However, for the methods using

Dirichlet conditions, the choice is more difficult since the gap in the spectrum is smaller.

Dirichlet Conditions. We consider the following equation with Dirichlet boundary conditions:

Boundary conditions may be in the form of

Dirichlet conditions,

Here we introduce the solution of 2D Laplace equation with

Dirichlet conditions in order to declare the basic idea of the method.

In this paper, we study the following gradient nonlinear elliptic system with

Dirichlet conditionsHe proposed that the homogeneous

Dirichlet conditions may be satisfied exactly by representing the solution as the product of two functions: (1) an real-valued function that takes on zero values on the boundary points; and (2) an unknown function that allows to satisfy (exactly or approximately) the differential equation of the problem.

In the article titled "On a Nonlinear Wave Equation Associated with

Dirichlet Conditions: Solvability and Asymptotic Expansion of Solutions in Many Small Parameters" [1], there are similarities with two of the authors' previous publications; one of them was cited:

Considering the

Dirichlet conditions at x = 0 and x = [x.sub.5] and the magnetic vector potential finite at y = +[infinity], the general solution of (1) can be expressed as

This field satisfies the

Dirichlet conditions at all four sides.

where [GAMMA] symbolizes the boundary, and the

Dirichlet conditions are considered at 20[degrees]C for natural convective air-cooling BEM formulation, Green's function as a solution of the Equation (2) through (7) as follows.

The inhomogeneous polyanalytic equation is studied by Begehr and Kumar [28] in D with

Dirichlet conditions and the following result is obtained.

Dirichlet conditions are assumed on a closed subset [[GAMMA].sub.D] of [GAMMA], while Neumann boundary conditions are assumed on [[GAMMA].sub.N] := [GAMMA]/[[GAMMA].sub.D].