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On Solvability of Boundary Value Problems for Kinetic Operator-Differential Equations

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Abstract

We study solvability of boundary value problems for the so-called kinetic operator-differential equations of the form B(t)u t −L(t)u = f, where L(t) and B(t) are families of linear operators defined in a complex Hilbert space E. We do not assume that the operator B is invertible and that the spectrum of the pencil L −λ B is included into one of the half-planes Re λ < a or Re λ > a \({(a\in {\mathbb{R}})}\). Under certain conditions on the above operators, we prove several existence and uniqueness theorems and study smoothness questions in weighted Sobolev spaces for solutions.

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Authors and Affiliations

  1. Ugra State University, Chekhov st. 16, 628012, Khanty-Mansiysk, Russia

    Sergey Pyatkov

  2. North-Eastern Federal University, Belinskii st. 58, 677000, Yakutsk, Russia

    Sergey Popov & Vasilii Antipin

Authors
  1. Sergey Pyatkov
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  2. Sergey Popov
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  3. Vasilii Antipin
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Correspondence to Sergey Pyatkov.

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Pyatkov, S., Popov, S. & Antipin, V. On Solvability of Boundary Value Problems for Kinetic Operator-Differential Equations. Integr. Equ. Oper. Theory 80, 557–580 (2014). https://doi.org/10.1007/s00020-014-2172-7

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  • DOI: https://doi.org/10.1007/s00020-014-2172-7

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