This paper builds on the initial work of Marsden and Scheurle on nonabelian Routh reduction. The main objective of the present paper is to carry out the reduction of variational principles in further detail. In particular, we obtain reduced variational principles which are the symplectic analogue of the well known reduced variational principles for the Euler{Poincar e equations and the Lagrange...

We derive a new variational principle in optics. We first formulate the principle for paraxial waves and then generalize it to arbitrary waves. The new principle, unlike the Fermat principle, concerns both the phase and the intensity of the wave. In particular, the principle provides a method for finding the ray mapping between two surfaces in space from information on the wave's intensity ther...

1. Abstract Equations governing the behavior of rectangular plates made of functionally graded materials (FGMs) are determined in this paper using the variational approach. Derivation of such equations is based on Reissner–Mindlin plate theory that is extended to handle two-constituent material distribution through the thickness. Material properties are assumed to vary with the power law in ter...

In this paper we derive a strain gradient plate model from the three-dimensional equations of strain gradient linearized elasticity. The deduction is based on the asymptotic analysis with respect of a small real parameter being the thickness of the elastic body we consider. The body is constituted by a second gradient isotropic linearly elastic material. The obtained model is recognized as a st...

This paper is concerned with the existence of two non-trivial weak solutions for a p(x)-Kirchho type problem by using the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle and the theory of the variable exponent Sobolev spaces.

We consider the following nonlinear singular elliptic equation −div (|x| −2a ∇u) = K(x)|x| −bp |u| p−2 u + λg(x) in R N , where g belongs to an appropriate weighted Sobolev space, and p denotes the Caffarelli–Kohn– Nirenberg critical exponent associated to a, b, and N. Under some natural assumptions on the positive potential K(x) we establish the existence of some λ 0 > 0 such that the above pr...

This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...

A general variational principle of classical fields with a Lagrangian containing field quantity and its derivatives of up to the N-order is presented. Noether’s theorem is derived. The generalized Hamilton-Jacobi’s equation for the Hamilton’s principal functional is obtained. These results are surprisingly in great harmony with each other. They will be applied to general relativity in the subse...

I find conditions under which the ”Weak Energy Principle” of Katz, Inagaki and Yahalom (1993) gives necessary and sufficient conditions. My conclusion is that, necessary and sufficient conditions of stability are obtained when we have only two mode coupling in the gyroscopic terms of the perturbed Lagrangian. To illustrate the power of this new energy principle, I have calculated the stability ...