Sentence examples for by a variational method from inspiring English sources

Free vibration analysis of isotropic Mindlin plates with edges elastically restrained against rotation and translation is carried out by a variational method.

A recent paper by Cordero-Erausquin and Klartag provides a characterization of the measures μ on Rd which can be expressed as the moment measures of suitable convex functions u, i.e. are of the form (∇u)#e−u for u Rd→R∪ and finds the corresponding u by a variational method in the class of convex functions.

To complete the proof by a variational method, we need the following mountain pass lemma.

By a variational method like [27], the existence and concentration of nontrivial solutions of (1.1) are established.

We get the first result by a variational method and critical point theory, and we get the second result by homology theory.

Motivated by the results of the above papers, we discuss the existence of nontrivial nonnegative solutions to Problem (1.1) by a variational method.

A size-dependent model for the electrostatically actuated Nano-Electro-Mechanical Systems (NEMS) incorporating nonlinearities and Casimir force is presented by using a variational method.

The problem of the non-linear buckling was solved by using a variational method for the asymptotic analytical numerical method (Koiter's theory).

Modifications to acoustic eigenmodes in combustion chambers such as those of liquid propellant rocket engines, produced by spatial variations of density and sound speed that arise mainly through progress of combustion processes, are analyzed by using a variational method.

A grid adapted to the solution is generated by using a variational method optimizing such important properties of a grid as smoothness, orthogonality, and grid cell volume variation simultaneously.

Recently, some researchers [27 31] have begun to study the existence of solutions for second-order differential delay equation by using a variational method.