Necessary and sufficient conditions for the solvability of a singular Dirichlet boundary problem for the Sturm-Liouville equation of general form

N. Chernyavskaya, L. Shuster

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the boundary problem −(r(x)y(x))+q(x)y(x)=f(x),x∈R, lim|x|→∞⁡y(x)=0 under the following conditions: 1) r>0,[Formula presented]∈L1loc(R),q∈L1loc(R); 2) equation (1) is correctly solvable in Lp(R), p∈(1,∞). We obtain necessary and sufficient requirements for the functions r and q under which, regardless of the choice of a function f∈Lp(R), p∈(1,∞), the solution y∈Lp(R) of equation (1) satisfies (2).

Original languageEnglish
Pages (from-to)1564-1601
Number of pages38
JournalJournal of Differential Equations
Volume416
DOIs
StatePublished - 25 Jan 2025

Keywords

  • Dirichlet problem
  • General Sturm-Liouville equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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