Spaces admissible for the sturm-liouville equation

N. A. Chernyavskaya, L. A. Shuster

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We consider the equation -y″(x) + q(x)y(x) = f(x); x ∈ R (1) where f ∈ Lloc p (R); p ∈ [1;1) and 0 q ∈2 Lloc 1 (R): By a solution of (1) we mean any function y; absolutely continuous together with its derivative and satisfying (1) almost everywhere in R: Let positive and continuous functions μ(x) and θ;(x) for x ∈ R be given. Let us introduce the spaces Lp(R;μ) = {f∈2 loc p (R) : //f//pLpp(R;μ) = /∞-∞ /μ(x)f(x)jpdx < 1∞}. Lp(R;θ) = {f ∈ Lloc p (R) : kfkp Lp(R;μ) = /∞-∞ /θ(x)f(x)/pdx <∞} : In the present paper, we obtain requirements to the functions f∈Lp and q under which 1) for every function f ∈ Lp(R;θ) there exists a unique solution (1) y ∈ Lp(R;μ) of (1); 2) there is an absolute constant c(p) ∈ (0;1) such that regardless of the choice of a function f ∈ Lp(R;θ) the solution of (1) satisfies the inequality //y//Lp(R;μ) c(p)kfkLp(R;θ):.

Original languageEnglish
Pages (from-to)1023-1052
Number of pages30
JournalCommunications on Pure and Applied Analysis
Issue number3
StatePublished - 1 May 2018


  • Admissible spaces
  • Sturm-liouville equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'Spaces admissible for the sturm-liouville equation'. Together they form a unique fingerprint.

Cite this