Sentence examples for established by applying from inspiring English sources

The uniqueness criterion is established by applying shooting method.

This result can be established by applying nonlinear alternative for single valued maps [18].

Their unknown distribution is established by applying continuity conditions at the interfaces, in all directions.

The joint probability distribution is established by applying the Parzen density estimator to the kernels.

Some new existence results of positive solutions are established by applying fixed-point index theory together with comparison theorem.

Then, well-posedness in H s with s > 3 / 2 was also established by applying Kato's semigroup theory.

In this study, the membership degree of each single factor is established by applying the dynamic clustering method.

Several existence and uniqueness results for the given problem are established by applying the tools of fixed-point theory.

The existence and uniqueness of iterative solution is established by applying the cone theory and the Banach contraction mapping principle.

The following result can be established by applying a similar argument as that in the proof of Theorem 3.2.

The following consequence can be established by applying the mountain pass theorem with Lemmas 3.4 and 3.6.