TY - JOUR

T1 - A criterion for correct solvability in Lp(ℝ) of a general Sturm-Liouville equation

AU - Chernyavskaya, N.

AU - Shuster, L.

PY - 2009/8

Y1 - 2009/8

N2 - We consider an equation-(r(x)y′(x))′+q(x)y(x)=f(x),x ∞ℝ, where f ∈ Lp(ℝ) for p ∈ (1, ∞) with the following conditions: r>0,q≥0,1/r ∈ L1 loc(ℝ) q ∈ L1loc(ℝ),∫ -∈0dt/r(t)= ∫0∈ dt/r(t)= ∞By a solution of the above-mentioned equations, we mean any function y that is absolutely continuous together with ry′ and satisfies it almost everywhere on . Under the above-mentioned conditions, we give a criterion for the correct solvability of the above-mentioned equation in L p(R) for p ∈ (1, ∞).

AB - We consider an equation-(r(x)y′(x))′+q(x)y(x)=f(x),x ∞ℝ, where f ∈ Lp(ℝ) for p ∈ (1, ∞) with the following conditions: r>0,q≥0,1/r ∈ L1 loc(ℝ) q ∈ L1loc(ℝ),∫ -∈0dt/r(t)= ∫0∈ dt/r(t)= ∞By a solution of the above-mentioned equations, we mean any function y that is absolutely continuous together with ry′ and satisfies it almost everywhere on . Under the above-mentioned conditions, we give a criterion for the correct solvability of the above-mentioned equation in L p(R) for p ∈ (1, ∞).

UR - http://www.scopus.com/inward/record.url?scp=68349137778&partnerID=8YFLogxK

U2 - 10.1112/jlms/jdp012

DO - 10.1112/jlms/jdp012

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AN - SCOPUS:68349137778

SN - 0024-6107

VL - 80

SP - 99

EP - 120

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 1

ER -