Sentence examples for established by using the from inspiring English sources

It can be easily established by using the following result.

The existence of nontrivial solution was established by using the nonlinear alternative of Leray-Schauder.

The uniqueness of solution was established by using the Banach contraction mapping principle.

Some new existence criteria of positive solutions are established by using the monotone iterative technique.

The results were established by using the fixed point theorem on a cone due to Krasnoselskii.

Theoretical results are established by using the oracle approach (see later).

Salinity and thermal gradient were properly established by using the salinity distribution methodology.

The dynamic equations of the CVBVS are established by using the generalized Lagrange's equation.

A homogenized plate model is first established by using the two-scale asymptotic expansion method.

The FLANN model can be established by using the Error Back-propagation algorithm.

Sufficient conditions for the global stability of the endemic equilibrium are established by using the comparison principle.