Sentence examples for minimal positive solution from inspiring English sources

The Laplace transform of the steady-state distribution of the buffer content is expressed through the minimal positive solution to a crucial equation.

We show that there exists ε⁎>0 such that no positive solutions exist when ε>ε⁎, while a minimal positive solution exists for every ε∈ 0,ε⁎).

The first solution is proved as the minimal positive solution, while the second one is obtained as the limit of a gradient flow whose starting point is properly chosen.

Problem (4.1) has minimal positive solution.

Infinite system (4.1) has a minimal positive solution satisfying for.

By Theorem 3.1, it follows that problem (4.1) has a minimal positive solution.

Now, we are in a position to show that (w^) and (nu^) are the maximal and minimal positive solutions of BVP (1.1) in ((0, dt^{alpha-1}]).

In this section, we shall prove the existence of maximal and minimal positive solutions for BVPHDEF (1) between the given upper and lower solutions on (J = [0, T ]).

In this section, we prove the existence of maximal and minimal positive solutions for FHDE (2.1) between the given upper and lower solutions on J = [ t 0, t 0 + a ].

That is to say, (u^{ast}) is a fixed point of the operator T. Now, we will show that (u^{ast}) and (v^{ast}) are the maximal and minimal positive solutions of the boundary value problem (1.1 - 1.2 1.1 - 1.2]).

Then BVP (1.1) has the maximal and minimal positive solutions (w^), (nu^) on J, such that 0