Sentence examples for for the auxiliary problem from inspiring English sources

Now we prove the uniqueness of solution for the auxiliary problem (3.1).

First, we give the existence theorem for the auxiliary problem for the problem (2.5).

First, an exact transform solution for the auxiliary problem of multiple-zone (integer n > 1) surface tractions is obtained.

To prove Theorem (1.5), we will first show the existence of a solution, say, for each for the auxiliary problem.

The complex potentials for the problem of an inclusion in an infinite body are given as two boundary integrals, and the boundary integral equation governing the complex potentials for the auxiliary problem is provided.

Recently, Dai [28] introduced a new class of generalized mixed variational like inequalities for random fuzzy mappings and established an existence theorem for the auxiliary problem and analyzed a new iterative algorithm for finding the solution of generalized mixed variational like inequality problems.

In this section, we extend the auxiliary principle technique to study problem (1.1) and prove the existence of solutions of the auxiliary problem for (1.1).

Let be the mapping such that for each, is the solution set of the auxiliary problem, that is,, (2.13).

Let be the mapping such that for each, is the solution set of the auxiliary problem MEP, that is, (2.9).

Based on these observations it can be concluded that any solution of the auxiliary problem (4) is a solution for the original problem (2) as well.

Let denote the solution of the auxiliary problem (3.1).