Abstract

We compare all existing methods of resolving the homogeneous differential inclusion problem. We emphasize that there is an elementary approach to construct solutions as limit of strongly convergent sequences of approximate solutions. We discuss which role plays an universal functional which measures maximal oscillations produced by admissible for the problem functions at a given one. We suggest a constructive way to generate stable solutions of the inclusions. Finally we prove higher regularity of solutions of the inclusions.

Author information

Contact details are reproduced from the original publication and may be historical.

Mikhail A. Sychev

Sobolev Institute for Mathematics, Koptuyg Avenue 4, Novosibirsk 630090, Russia

masychev@math.nsc.ru

Keywords

  • Functional analysis
  • calculus of variations
  • PDE
  • differential inclusions
  • sequences obtained by almost maximal perturbations
  • stable solutions
  • higher regularity

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Suggested citation

M. A. Sychev. “Comparing Various Methods of Resolving Differential Inclusions.” Journal of Convex Analysis 18 (2011), No. 4, 1025–1045. https://doi.org/10.68381/jca18063

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.