Sentence examples for principle of symmetric from inspiring English sources

69 (1979) 19) gave some sufficient conditions to guarantee the so-called "Principle of Symmetric Criticality": every critical point of J restricted on the subspace of G-symmetric points becomes also a critical point of J on the whole space X.

Principle of symmetric criticality.

Applying the principle of symmetric criticality, we obtain that ((u_{1}, v_{1})) is a nontrivial G-invariant solution of problem ((mathscr{P}_{sigma}^{overline{Q}})).

Now we give the proof of Theorems 2.1 and 2.2 by applying the fountain theorem and the principle of symmetric criticality.

In Section 2 we introduce some notation and state some well-known results, such as the principle of symmetric criticality and the mountain pass theorem.

Using the principle of symmetric criticality [21], we can look for critical points of I restricted on (W_{0,G}^{1,p}(S)).

Dynamically equivalent excitations are utilized to formulate a dynamic version of Saint-Venant's principle for symmetric excitations with frequencies below the first cut-off frequency of a strip.

This idea of interaction is a generalized symmetric principle of definitional reflection.

Hereby, we directly apply the reflection method based on the principle of the so-called symmetric extension, which seems simpler than that used in [7].

So we prefer to transform directly a ({P H}_{ 0}) problem into a ({P R}_{n,n}) problem by using the reflection method based on the principle of the so-called symmetric extension [18].

By utilizing the standard variational approach, together with the symmetric criticality principle of Palais [11], the authors in [10] attained several valuable symmetric results to problem (1.2) under different conditions on the weighted function (K x)).