Sentence examples for by introducing a variational from inspiring English sources

Very recently, by introducing a variational framework for a class of second-order nonlinear differential equations with non-separated periodic boundary value conditions, Han [21] obtained some results on the existence of non-trivial, positive, and negative solutions of problem (1.2), where the nonlinearities are unbounded and satisfy Ahmad-Lazer-Paul type conditions.

Fang and Huang [8] studied variational inclusions by introducing a class of generalized monotone operators, called H-monotone operators and defined the associated resolvent operator.

The new iterative method is a hybrid of variational iteration method and the Adomian decomposition method and further refined by introducing a new correction functional.

The most common of these mixed formulations is the Lagrange Multiplier (LM) method, a two-field variational approach which has been used widely to enforce incompressibility of the myocardium by introducing a variable to respresent the hydrostatic pressure [16,17,4,19,44].

This new correction functional is obtained from the standard correction functional of variational iteration method by introducing an auxiliary parameter γ in it.

First, we introduce a variational setting for problem (P).

An extension of CPT represents the variational cluster approach (VCA, [6]) which improves the results by introducing variational parameters.

Recently, Censor et al. [23] introduced a new variational inequality problem which we call the split variational inequality problem (SVIP).

This paper introduces a novel variational method for ultrasound image denoising for speckle suppression and edge enhancement.

In 2009, Noor [10] introduced a nonconvex variational inequalities based on the uniformly prox-regular sets.

By introducing this expansion into the variational principle, an equivalent coupled-mode system of horizontal equations is derived, fully accounting for the effects of nonlinearity and dispersion.