Sentence examples for points of the functional from inspiring English sources

The critical points of the functional Fn=||m||2 : PVn↦R are studied, in order to understand the stratification of Ln⊂PVn defined by the negative gradient flow of Fn, where Ln is the algebraic subset of all Lie algebras.

Thus the critical points of the functional F w) coincide with the weak solutions of (2.2).

Hence, critical points of the functional φ are classical (2ktau -periodic solutions of system (1.1).

The weak solutions of (3.1) are critical points of the functional defined by (3.3).

In fact, the critical points of the functional (I_{lambda}) are the weak solutions of (2.1).

By Clarke's Theorem 10, there exist at least m pairs of different critical points of the functional ϕ.

It is well known that the solutions of (1.1) are precisely the critical points of the functional (J u)).

Finally, we construct the control functions by the minimum point of the functional and get the approximate controllability.

Lemma 2.8 If the function u ∈ H is a critical point of the functional φ, then u is a solution of system (1.1).

If function (u(t)in H) is a critical point of the functional φ, then (u(t)), (tin[0,T]) is a solution of the system (1.1).

Let be a critical point of the functional.