Sentence examples for by variational method using from inspiring English sources

The following equation is obtained by variational method using wave functions χ z): (26).

In order to test the method, the transport coefficients, i.e. thermal conductivity and viscosity for all noble gases, are calculated and compared with those obtained by the variational method using the Sonine polynomials expansion.

This differential equation is solved for different initial conditions by variational method by using Lagrange Hamilton type principle.

We obtain this result by approaching the variational method and using the generalized mountain pass theorem for the fourth order elliptic problem with bounded nonlinear term.

We prove Theorem 1.1 by approaching the variational method and using the mountain pass theorem for the reduced fourth order elliptic problem with bounded nonlinear term.

has been studied by using variational method.

We prove the existence of periodic solutions under a generalized Lazer-Leach type condition by using variational method.

They proved that IBVP (1.4) has at least one solution and infinitely many solutions by using variational method and critical point theorem.

Motivated by the above facts, in this paper, our aim is to study the variational structure of IBVP (1.1) in an appropriate space of functions and obtain the existence and multiplicity of solutions for IBVP (1.1) by using variational method.

In this paper, by using variational method, we have dealt with a kind of ordinary p-Laplacian system and obtained the existence of fast homoclinic solutions to the above system.

By using variational methods, the problems can be formulated via either "early discretization" or "late discretization" approach.