Some problems in the Calculus of Variations
Journal Title: Annales Mathematicae Silesianae - Year 2017, Vol 31, Issue
Abstract
We present some results and open problems in the Calculus of Variations.
Authors and Affiliations
Arrigo Cellina
We present some results and open problems in the Calculus of Variations.
Arrigo Cellina
Multipliers of uniform topological algebras
Let $E$ be a complete uniform topological algebra with Arens-Michael normed factors $(E_α)_{α∈Λ}$. Then $M(E)\cong\lim_{←}M(E_α)$ within an algebra isomorphism $φ$. If each factor $E_α$ is complete, then every multiplier...
A note on additive groups of some specific associative rings
Almost complete description of abelian groups $(A,+,0)$ such that every associative ring $R$ with the additive group $A$ satisfies the condition: every subgroup of $A$ is an ideal of $R$, is given. Some new results for $...
Strong unique ergodicity of random dynamical systems on Polish spaces
In this paper we want to show the existence of a form of asymptotic stability of random dynamical systems in the sense of L. Arnold using arguments analogous to those presented by T. Szarek in [6], that is showing it usi...
On computer-assisted proving the existence of periodic and bounded orbits
We announce a new result on determining the Conley index of the Poincaré map for a time-periodic non-autonomous ordinary differential equation. The index is computed using some singular cycles related to an index pair of...
The behaviour of weak solutions of boundary value problems for linear elliptic second order equations in unbounded cone-like domains
We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find...