We revisit the classical problem of the buckling of a long thin axially compressed cylindrical shell. By examining the energy landscape of the perfect cylinder, we deduce an estimate of the sensitivity of the shell to imperfections. Key to obtaining this estimate is the existence of a mountain pass point for the system. We prove the existence on bounded domains of such solutions for almost all ...

Correspondence should be addressed to Yongkun Li, [email protected] Received 16 December 2010; Revised 6 February 2011; Accepted 11 February 2011 Academic Editor: Dumitru Motreanu Copyright q 2011 Y. Li and T. Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the...

Abstract. We study the boundary value problem −div((|∇u|1 + |∇u|2)∇u) = f(x, u) in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in R . We focus on the cases when f±(x, u) = ±(−λ|u| u+ |u|u), where m(x) := max{p1(x), p2(x)} < q(x) < N ·m(x) N−m(x) for any x ∈ Ω. In the first case we show the existence of infinitely many weak solutions for any λ > 0. In the second case we prove that if λ is...

A deformation lemma for functionals which are the sum of a locally Lipschitz continuous function and of a concave, proper and upper semicontinuous function is established. Some critical point theorems are then deduced and an application to a class of elliptic variational-hemivariational inequalities is presented. Introduction It is by now well known that the Mountain Pass Theorem of Ambrosetti ...

The well-known forking lemma by Pointcheval and Stern has been used to prove the security of the so-called generic signature schemes. These signature schemes are obtained via the Fiat-Shamir transform from three-pass identification schemes. A number of five-pass identification protocols have been proposed in the last few years. Extending the forking lemma and the Fiat-Shamir transform would all...

An integral inequality is deduced from the negation of the geometrical condition in the bounded mountain pass theorem of Schechter, in a situation where this theorem does not apply. Also two localization results of non-zero solutions to a superlinear boundary value problem are established.

We establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter λ, we consider the system −∆v = λf(u) in Ω, −∆u = g(v) in Ω, u = v = 0 on ∂Ω, where Ω is a smooth bounded domain in R with N ≥ 1. One solution is obtained applying Ambrosetti and Rabinowitz’s classical Mountain Pass Theorem, and t...

The existence of homoclinic orbits is obtained for a class of the second order Hamiltonian systems ü(t)−L(t)u(t)+∇W (t,u(t)) = 0, ∀t ∈ R , by the mountain pass theorem, where W(t,x) needs not to satisfy the global (AR) condition. Mathematics subject classification (2000): 34C37, 37J45, 47J30, 58E05.

We consider an eigenvalue problem for a certain type of quasi-linear second-order di®erential equation on the interval ð0;1Þ. Using an appropriate version of the mountain pass theorem, we establish the existence of a positive solution in H 1 0 ð0;1Þ for a range of values of the eigenvalue. It is shown that these solutions generate solutions of Maxwell's equations having the form of guided trave...

These notes are designed to serve as a template of a LaTeX article. In the process we will describe some notions of Geometric Analysis pertaining to the Mountain Pass Theorem. Little attempt was made to be a publishable set of notes, but instead to provide examples of commonly used commands, environments, and symbols in LaTeX.