Admissible pair of spaces for non-correctly solvable linear differential equations

Nina A. Chernyavskaya, Lela S. Dorel, Leonid A. Shuster

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We consider the differential equation [Presented Equation] Under these conditions, the above equation is not correctly solvable in Lp(ℝ) for any p ϵ [1, ∞). Let q∗(x) be the Otelbaev-type average of the function q(t), t ∞ ℝ, at the point t = x; let θ(x) be a continuous positive function for x ϵ ℝ, and [Presented Equation] We show that if there exists a constant c ϵ [1, ∞) such that the inequality c-1q∗(x) ≤ θ(x) ≤ cq∗(x) holds for all x ϵ ℝ, then under some additional conditions for q the pair of spaces {Lp,θ(ℝ); Lp(ℝ)} is admissible for the considered equation.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalJournal of Applied Analysis
Issue number1
StatePublished - 1 Jun 2016

Bibliographical note

Publisher Copyright:
© 2016 by De Gruyter.


  • Linear differential equation
  • admissible pair
  • non-correctly solvable differential equation


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