During the last twenty years, many minimax theorems that have proved to be very useful tools in finding critical points of functionals have been established. They have all in common a geometric intersection property known as the linking principle. Our purpose in this paper is to give a linking theorem that strengthens and unifies some of these works. We think essentially to Ambrosetti-Rabinowit...

Ekeland and Scheinkman (1986) prove the necessity of a standard transversality condition under certain technical conditions. Their result is one of the most powerful on the necessity of a transversality condition currently available in the literature, and their proof involves numerous estimations and relies on Ekeland’s variational principle and Fatou’s lemma. This note relaxes some of their as...

The extended variational principle fails for non-holonomic case. We use a vertical rolling disk as an example to illustrate this failure. We have studied the fundamental dynamical principle from which the motion of a mechanical system, whether holonomic or non-holonomic, can be derived.

A variational principle governing the dynamics of a vortex filament in unbounded incompressible inviscid fluid flow was suggested by Rasetti and Regge [Physica A 80, 217 (1975)]. This variational principle holds in the approximation taking into account the logarithmically large terms, on the order of ln(La) , L and a being the length and the cross-section radius of the filament, respectively. I...

A variational principle is constructed for gravity coupled to an asymptotically linear dilaton and a p-form field strength. This requires the introduction of appropriate surface terms – also known as ‘boundary counterterms’ – in the action. The variation of the action with respect to the boundary metric yields a boundary stress tensor, which is used to construct conserved charges that generate ...

In this paper we investigate optimal control problems governed by variational inequalities. We present a method for deriving optimality conditions in the form of Pontryagin's principle. The main tools used are the Ekeland's variational principle combined with penalization and spike variation techniques. 1. Introduction. The purpose of this paper is to present a method for deriving a Pontryagin ...

X iv :p hy si cs /9 90 30 15 v1 [ ph ys ic s. cl as sph ] 9 M ar 1 99 9 Unified Descriptions Of All Integral Variational Principles Y. C. Huang 1 A. M. Li M. X. Shao X. G. Li Department of Applied Physics, Beijing Polytechnic University, Beijing 100022, P. R. China Department of Physics, Beijing Normal University, Beijing 100082, P. R. China INFN, Sezione di Catania, Corso Italia 57, I-95129 Ca...