Sentence examples for methods we establish from inspiring English sources

Using variational methods, we establish conditions for the nonlinear stability of adhesive states between an elastica and a rigid halfspace.

By means of variational methods we establish existence and multiplicity of solutions for a class of nonlinear nonlocal problems involving the fractional p-Laplacian and a combined Sobolev and Hardy nonlinearity at subcritical and critical growth.

Based upon the symmetric criticality principle of Palais and variational methods, we establish several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the weighted functions and the parameters.

To prove that the ((mathit{PS})) sequence weakly converges to a critical point of the corresponding functional, we adapt ideas developed by [10 12] and then by variational methods, we establish the existence of infinitely many high-energy solutions to problem (1.1) with a concave-convex nonlinearity, i.e., (f x,u =lambda h_{1}(x)|u|^{m-2}u+h_{2}(x)|u|^{q-2}u), (1< m< p< q< p_=frac{pN}{N-2p}).

The methods we establish here can form the basis for such research.

Using sensitive sequence profile comparison methods we establish that the PafA family proteins are related to the γ-glutamyl-cysteine synthetase and glutamine synthetase.

Methods: We established an adsorbent-based PMB release system which ensures a constant PMB level in plasma during extracorporeal therapies.

To have a reference point to compare the methods, we established a defined signalling period (DSP).

Using parsimony and ML methods, we established that non-claustral behavior is the most likely ancestral condition.

Materials and methods: We established a P19 embryonal carcinoma cell-based experimental system, which profits from two similar differentiation protocols producing endodermal or neuroectodermal lineages.

"We handed the action plan with all the accompanying materials over to them, and they continued their work in line with the plan and the methods we established", said Dervišević.