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On inverses of δ -convex mappings

Jakub Duda (2001)

Commentationes Mathematicae Universitatis Carolinae

In the first part of this paper, we prove that in a sense the class of bi-Lipschitz δ -convex mappings, whose inverses are locally δ -convex, is stable under finite-dimensional δ -convex perturbations. In the second part, we construct two δ -convex mappings from 1 onto 1 , which are both bi-Lipschitz and their inverses are nowhere locally δ -convex. The second mapping, whose construction is more complicated, has an invertible strict derivative at 0 . These mappings show that for (locally) δ -convex mappings...

On Ishlinskij's model for non-perfectly elastic bodies

Pavel Krejčí (1988)

Aplikace matematiky

The main goal of the paper is to formulate some new properties of the Ishlinskii hysteresis operator F , which characterizes e.g. the relation between the deformation and the stress in a non-perfectly elastic (elastico-plastic) material. We introduce two energy functionals and derive the energy inequalities. As an example we investigate the equation u ' ' + F ( u ) = 0 describing the motion of a mass point at the extremity of an elastico-plastic spring.

On noncompact perturbation of nonconvex sweeping process

Myelkebir Aitalioubrahim (2012)

Commentationes Mathematicae Universitatis Carolinae

We prove a theorem on the existence of solutions of a first order functional differential inclusion governed by a class of nonconvex sweeping process with a noncompact perturbation.

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