On the theorem of Filippov-Pliá and some applications

Tzanko Donchev*, Elza Farkhi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In the paper some known and new extensions of the famous theorem of Filippov (1967) and a theorem of Pliś (1965) for differential inclusions are presented. We replace the Lipschitz condition on the set-valued map in the right-hand side by a weaker onesided Lipschitz (OSL), one-sided Kamke (OSK) or a continuity-like condition (CLC). We prove new Filippov-type theorems for singularly perturbed and evolution inclusions with OSL right-hand sides. In the CLC case we obtain two extended theorems, one of which implies directly the relaxation theorem. We obtain also a theorem in Banach spaces for OSK multifunctions. Some applications to exponential formulae are surveyed.

Original languageEnglish
Pages (from-to)1251-1271
Number of pages21
JournalControl and Cybernetics
Issue number4
StatePublished - 2009


  • Differential inclusions
  • Filippov
  • Kamke
  • Lipschitz
  • One-sided
  • Pliś


Dive into the research topics of 'On the theorem of Filippov-Pliá and some applications'. Together they form a unique fingerprint.

Cite this