Sentence examples for exists one solution from inspiring English sources

Thus, all the conditions of Theorem 3.1 are satisfied, and consequently there exists one solution for problem (3.7 - 3.8 3.7 - 3.8]).

Let assumptions (i) and (ii) hold, then for each there exists one solution of initial problem (1.1) such that (2.1).

We will assume that there exists one solution of system (2) which is denoted by x m, 0, φ), or, x(m), if no confusion occurs.

For small input amplitudes I we have N ′ ( 0 ) > 0 and there always exists one solution branch for α β < γ c ≈ 0.06.

Combining some sign conditions and the lower and upper solution method, we obtain the existence of solutions when there exists one lower solution or one upper solution.

Then there exists one unique solution to problem (3.1) and on.

According to Property 2.1, we can see that, for any (uinmathcal {U}_{a}), there exists one unique solution satisfying system (1) and denote it as (x t)=x t,u)).

Given and, then there exists one and only one solution of (1.1) such that (2.27).

Therefore, there exists one and only one solution provided that g < 1.

Given and, then there exists one and only one solution of (1.3) such that.

In addition, if f is the same degree polynomial to g then there exists one and only one solution.