Sentence examples for use of variational methods from inspiring English sources

This dependence on the gradient prevents the use of variational methods directly on equation (1.1).

These requirements need to develop a nonstandard approach, in particular prevent the use of variational methods.

In the 1989 paper of Rabinowitz [1], we find the first substantial use of variational methods to study heteroclinic orbits for Hamiltonian systems.

Essential features of the present work are the dependence on the gradient ∇u, which prevents the use of variational methods, and the unboundedness of the domain, which produces lack of compactness.

As an application, we will discuss the existence of nontrivial solutions to the p-Laplace equations with resonance on the Fučik spectrum by making use of variational methods and Morse theory.

Recently, there is a large literature on the use of variational methods to the existence of homoclinic or heteroclinic orbits of Hamiltonian systems; see [2 7] and the references therein.

The existence of new periodic solutions with a prescribed energy is established by the use of constrained variational methods.

In recent years, many authors have studied the existence of solutions of the fractional boundary value problems (FBVPs for short) by use of the variational method [18 25].

By use of the variational method, the effect is proved under the assumptions that pair potentials fall off with order O(¦x¦−ϱ), ϱ > 2, at infinity and that all three two-body subsystems have a zero resonance energy.

Recently, some authors have studied the existence of solutions of IBVPs using variational methods.

We will use the variational methods to solve the problem of (1.1).