Sentence examples for unique system of solutions from inspiring English sources

Then there exists a unique system of solutions ( x, y ) to BVPs (2.8).

The system of equations (9) has a unique system of solutions if the following condition holds: biggl( 1 - frac{2(1 - rho)}{(2 - rho)M rho)}gamma_{1} - frac{2 rho }{(2 - rho)M rho)} gamma_{1}t biggr) ge 0. (36).

In the next section, the unique existence of solutions for system (1.3) is established.

Moreover, the optimal treatment allocation is characterized by a unique set of solutions to a system of equations.

If the right-hand side of system (2) satisfies a Lipschitz condition in (x t)), (y(t)), (z(t)), (w(t)) and (x t-r)), and there ex t-rsolutions of system (2), then it is the unique solution of system (2).

In Section 4, we establish sufficient conditions for the global attractivity of a unique almost periodic solution of system (1.1) and system (1.4) without delays by means of Lyapunov functional.

In Section 2 we demonstrate and prove the main results of the paper, such as the existence of a unique positive solution of the system, sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, persistence in the mean and stochastic permanence of the system.

Obviously, the existence of a unique almost periodic solution of system (2.1) is equivalent to that of system (3.2).

For any given initial conditions satisfying (4), there exists a unique solution of system (2) defined on ([ 0,+infty) ), and this solution remains non-negative and bounded for all (tgeq 0 ). Moreover, we have N t)leq N 0)+frac{Lambda }{mu }, where (N t)=S t)+I t)).

In Section 2, we show there is a unique positive solution of system (1.3).

Using Theorem 2.2.1 from [29], we can state that there is a unique local solution of system (1 - 2).