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Periodic solutions to Lagrangian system

Oleg Zubelevich — 2018

Commentationes Mathematicae Universitatis Carolinae

A classical mechanics Lagrangian system with even Lagrangian is considered. The configuration space is a cylinder m × 𝕋 n . A large class of nonhomotopic periodic solutions has been found.

A note on existence theorem of Peano

Oleg Zubelevich — 2011

Archivum Mathematicum

An ODE with non-Lipschitz right hand side has been considered. A family of solutions with L p -dependence of the initial data has been obtained. A special set of initial data has been constructed. In this set the family is continuous. The measure of this set has been estimated.

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