The problem under consideration is as follows. Let I(u, ω) be a random functional of u , u is an element of some functional space R, ω being a random parameter. For each ω, one seeks for a minimum value of the functional I(u, ω). The minimizing element, ǔ, of the functional I(u, ω) is random since it depends on ω. We are interested in determining the probability density function of some determi...

In this paper we present a novel variational approach to the question of existence and multiplicity of positive solutions to semipositone problems in a bounded smooth domain of RN . We consider both the sublinear and superlinear cases.

We consider the class of curves of finite total curvature, as introduced by Milnor. This is a natural class for variational problems and geometric knot theory, and since it includes both smooth and polygonal curves, its study shows us connections between discrete and differential geometry. To explore these ideas, we consider theorems of Fáry/Milnor, Schur, Chakerian and Wienholtz.

1550-7998=20 In a recent article, W.-S. Hou and G.-G. Wong [Phys. Rev. D 67, 034 003 (2003)] have investigated the spectrum of two-gluon glueballs below 3 GeV in a potential model with a dynamical gluon mass. We point out that, among the 18 states calculated by the authors, only three are physical. The other states either are spurious or possess a finite mass only due to an arbitrary restrictio...

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In this short survey we recall some basic results and relations between the qualitative theory of linear ordinary differential equations with real time and the reality problems in Schubert calculus. We formulate a few relevant conjectures.

In 1926 M. Lavrentiev [7] proposed an example of a variational problem whose infimum over the Sobolev spaceW, for some values of p ≥ 1, is strictly lower than the infimum overW1,∞. This energy gap is known since then as the Lavrentiev phenomenon. The aim of this paper is to provide a deeper insight into this phenomenon by shedding light on an unnoticed feature. Any energy that presents the Lavr...

In this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent processes.

We provide a proof for a Perron-type theorem on the principal eigenvalue of nonsymmetric elliptic operators based on the strong maximum principle. This proof is modeled after a variational proof of Perron’s theorem for matrices with positive entries that does not appeal to Perron-Frobenius theory.

In this paper we study the existence of the eigencurves of the p-Laplacian with indefinite weights. We obtain also their variational formulations and asymptotic behavior.