A differential coercivity result is established for a class of order nonsmooth functionals fulfilling an appropriate Palais-Smale condition. The core of this approach is an asymptotic type statement involving such functionals, obtained by means of the monotone variational principle in Turinici [An. Şt. UAIC Iaşi, 36 (1990), 329-352].

Article history: Received 16 January 2014 Accepted 20 September 2014 Available online 22 October 2014 Submitted by Y. Wei MSC: 15A18 15A57

We discuss restrictions of two-dimensional translation-invariant Gibbs measures to a one-dimensional layer. We prove that there exists a translation invariant a.s. absolutely convergent potential making these restrictions into weakly Gibbsian measures. We discuss the existence of the thermodynamic functions for this potential and the variational principle for the weakly Gibbsian measures.

Recently, Wazwaz [Appl. Math. Comput. 118 (2001) 311–325] applied the Adomian s decomposition method to solve analytically the solution of sixth-order boundary value problems. The same problem is discussed via the variational principle, which reveals to be much more simpler and much more efficient. 2002 Elsevier Science Inc. All rights reserved.

We discuss restrictions of two-dimensional translation-invariant Gibbs measures to a one-dimensional layer. We prove that there exists a translation invariant a.s. absolutely convergent potential making these restrictions into weakly Gibbsian measures. We discuss the existence of the thermodynamic functions for this potential and the variational principle for the weakly Gibbsian measures.

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.