Sentence examples for boundary value problem we from inspiring English sources

Now, proceeding as in the proof of the initial boundary value problem, we get (23).

In order to solve the initial boundary value problem we will use the Laplace transform technique.

If we write the complex conjugate of this boundary value problem, we obtain the following boundary value problem: (24).

To establish the existence of a solution for the boundary value problem, we need to make the following assumptions.

For the original boundary value problem we consider twelve cases, (see Table 1 in the Appendix), each of which has s+l+m+1 eigenvalues.

As applications, using Lemma 3.9 and the results of the boundary value problem, we consider two kinds of singular integral equations and obtain their explicit representations of solutions.

On the integral boundary value problems, we refer to [26 30].

For more knowledge about the boundary value problems, we refer the reader to [11] [28].

We refer to the results [2 5, 12, 14] and for periodic boundary value problems we cite [15 17].

Among a substantial number of works dealing with right focal boundary value problems, we mention [1 16, 18 25].

Among a substantial number of works dealing with fourth-order boundary value problems, we mention [1, 3 31].