Perturbation results for multivalued linear operators

Ronald Cross*, Angelo Favini, Yakov Yakubov

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


We give some perturbation theorems for multivalued linear operators in a Banach space. Two different approaches are suggested: the resolvent approach and the modified resolvent approach. The results allow us to handle degenerate abstract Cauchy problems (inclusions). A very wide application of obtained abstract results to initial boundary value problems for degenerate parabolic (elliptic-parabolic) equations with lower-order terms is studied. In particular, integro-differential equations have been considered too.

Original languageEnglish
Title of host publicationProgress in Nonlinear Differential Equations and Their Application
PublisherSpringer US
Number of pages20
StatePublished - 2011

Publication series

NameProgress in Nonlinear Differential Equations and Their Application
ISSN (Print)1421-1750
ISSN (Electronic)2374-0280


  • Degenerate equation
  • Elliptic-parabolic equation
  • Modified resolvent
  • Multivalued linear operators
  • Parabolic equation
  • Perturbation
  • Resolvent
  • Selection


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