Weight summability of solutions of the Sturm-Liouville equation

N. Chernyavskaya, L. Shuster

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We consider an equation -y″(x)+q(x)y(x)=f(x), x∈R; (1) where f(x)∈Lp(R), p∈[1,∞] (L(R):=C(R)), 1≤q(x)∈Lloc1(R). We study requirements for a weight function r(x)∈Llocp(R) and for q(x) under which, for a given p∈[1,∞], regardless of f(x)∈Lp(R), the solution y(x)∈Lp(R) of Eq. (1) satisfies the inequalities: r(x)y(x)p≤cf(x)p, y″(x)p+q(x)y(x)p≤c f(x)p, c=const.

Original languageEnglish
Pages (from-to)456-473
Number of pages18
JournalJournal of Differential Equations
Volume151
Issue number2
DOIs
StatePublished - 20 Jan 1999

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