Sentence examples for unique solution of this from inspiring English sources

Under suitable continuity and compatibility conditions on the data, a unique solution of this problem exists.

Taking into account that the unique solution of this equation is x = 0, we have proved that T has a unique best proximity point which is ( 0, 0,).

Since is the unique solution of this problem with by Remark 2.2, we have for each and any solution of problem (2.25), (1.2).

In Section 3, one kind capillarity equation is discussed, from which we can see the connection among the unique solution of this equation, the unique solution of one kind variational inequality and the iterative algorithm presented in Section 2.

We first obtain the unique solution of this problem using Fourier method of separation of variables with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem under certain conditions [12].

We first obtain the unique solution of this problem using the Fourier method of separation of variables with respect to the eigenfunctions of the corresponding Sturm-Liouville eigenvalue problem under certain conditions [18].

(3.18) This x̃ is the unique solution of the optimization problem (1.4).

This solution is thus the unique solution of the Lyapunov equation.

This implies that there exists a unique solution of the nonlinear Fredholm integral equation (4.1).

Then, converges strongly to the unique solution of the unique solutions of the variational inequality (1.11).

Moreover, x̃ is the unique solution of the VIP (3.2).