Sentence examples for based on variational methods from inspiring English sources

In [16] one studies a variant of the p-Laplacian equation with an approach based on variational methods, in [17] one studies the eigenvalues of the Dirichlet problem, and in [18] one finds some oscillation criteria for equations with the p-Laplacian.

The analysis is based on variational methods and on the Hypercircle theorem of the linear theory of elasticity.

The proof is based on variational methods.

The approach is based on variational methods.

This work is mainly based on variational methods.

Based on variational methods, some new results are obtained in regard to the existence of solutions.

We now sketch our proofs of Theorems 1.2, 1.5 and 1.7 based on variational method.

Based on variational method, we introduce a different concept of solution, that is, a weak solution to problem (1.1).

Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here.

Based on variational principle our method can generate surfaces by minimizing the objective function newly proposed in this paper for given arbitrary boundary curves.

The proposed method is based on variational data assimilation and adjoint-based optimization.