Sentence examples for uses variational methods to from inspiring English sources

Variational principle is applied to functional F depending on several variable functions and uses variational methods to find extremum of the functional.

We use variational methods to prove the existence of spikes around saddle points of the potential V x).

We consider the problem (1.1) and use variational methods to get positive solutions.

Kindermann et al. used variational methods to understand the nonlocal means filter [20].

In this paper, we use variational methods to investigate the solutions of impulsive differential equations with Sturm-Liouville boundary conditions.

In this paper, we use variational methods to investigate the solutions of impulsive differential equations on the half-line.

For the case α = 1, Euler [3 5] studied (1.1 - 1.3 1.1 - 1.3n't use variational methods to study periodic solutions.

On the other hand, many researchers have used variational methods to study the existence of solutions for boundary value problems [15 21].

On the other hand, many researchers used variational methods to study the existence of solutions for impulsive boundary value problems on the finite intervals [13 19].

In the present paper, we use variational methods to prove two existence results of nontrivial solutions for the Schrödinger-Kirchhoff-type problem.

Recently, few researchers have used variational methods to study the existence of solutions for impulsive differential equations with Dirichlet boundary conditions [15, 16].