Sentence examples for boundary value problem given from inspiring English sources

Let us now combine the idea of a non-binary-valued confidence function c with the mixed boundary value problem given in (2).

By changing the boundary condition, the boundary value problem given on the random domain can be transformed into a boundary value problem on a fixed domain.

The boundary value problem given by Eqs.

Consequently, we have the following unique solution of the boundary value problem given by Eqs.

This section is devoted to the solvability of the fractional boundary value problem given in (5).

Hence, the boundary value problem given by obeying (2.2) with (4.1) has eigenvalues.

Here, we have successfully addressed the problem involving the existence and uniqueness of positive and nondecreasing solutions of a family of fractional q-difference boundary value problems given by Eqs.

In a similar manner, we now prove that the transformed boundary value problems given in Theorem 4.1 have eigenvalues, that is, the spectrum increases by one in each case.

The following paragraph needs to be inserted immediately after Theorem 4.2: It is important to note that the spectral parameter in the original boundary value problems given in cases (1 - 9) of Table 1 for Theorem 4.2 must first, without loss of generality, be shifted so as to ensure that all the eigenvalues are greater than zero.

An algorithm is developed for discretizing boundary-value problems given by a general linear elliptic second order partial-differential equation with general mixed or Robin boundary conditions in general logically rectangular grids.

The Green function of fractional differential equation boundary value problem is given by.