Regular boundary value problems for ordinary differential-operator equations of higher order in umd banach spaces

Angelo Favini, Yakov Yakubov

Research output: Contribution to journalArticlepeer-review

Abstract

We prove an isomorphism of nonlocal boundary value problems for higher order ordinary differential-operator equations generated by one operator in UMD Banach spaces in appropriate Sobolev and interpolation spaces. The main condition is given in terms of R-boundedness of some families of bounded operators generated by the resolvent of the operator of the equation. This implies maximal L p-regularity for the problem. Then we study Fredholmnees of more general problems, namely, with linear abstract perturbation operators both in the equation and boundary conditions. We also present an application of obtained abstract results to boundary value problems for higher order elliptic partial differential equations.

Original languageEnglish
Pages (from-to)595-614
Number of pages20
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume4
Issue number3
DOIs
StatePublished - Jun 2011

Keywords

  • Abstract elliptic equation
  • Fredholmness
  • Higher order
  • Isomorphism
  • R-boundedness
  • Regular problem
  • UMD Banach space

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