Sentence examples for establish by using the from inspiring English sources

The main trait of this free boundary problem is that it is essentially multidimensional, so that its well-posedness is hard to establish by using the usual methods in the classical theory of free boundary problems.

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

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

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

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

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

The finite element model is established by using the commercial general purpose computer package ANSYS.

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

A hydrodynamic model was established by using the Chebyshev polynomial fitting method.