Sentence examples for by using standard arguments from inspiring English sources

As an application, we have the following corollary by using standard arguments as in [15], Theorem 3.3.

By using standard arguments, we can easily show that T : C [ 0, 1 ] × C [ 0, 1 ] → C [ 0, 1 ] × C [ 0, 1 ] is linear completely continuous.

Since local existence results can be proved by using standard arguments, say, Galerkin method, we only deal with the a priori estimates.

By using standard arguments, we can easily show that (Q_{1}), (Q_{2}) and (Q_{3}) are completely continuous (continuous and compact, that is, map bounded sets into relatively compact sets), and then Q is a completely continuous operator.

When the input is (I t)=(I_{1}(t),I_{2}(t),ldots,I_{n}(t))^{T}= 0,0,ldots,0)^{T}), by using standard arguments as Theorem 3.1, we can derive the stability conditions for system (2.1).

When the control input (J t)=(J_{1}(t),J_{2}(t),ldots,J_{n}(t))^{T}= 0,0,ldots,0)^{T}), by using standard arguments as Theorem 3.2, we can derive the stability conditions for system (3.8).

On the other hand, taking for any, by sublinear growth condition on one easily examine by using standard argument that the perturbed system (3.25). is not dissipative.

When (12) holds, the proof can be presented using standard arguments similar to the proof above.

The following result can be proved using standard arguments as in [26, 28].

Furthermore, using standard arguments, we obtain the functional is functional in and (3.3).

In order to prove this theorem, we use standard arguments of density.