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Solvability in Lp of the Neumann problem for a singular non-homogeneous Sturm-Liouville equation

Part of: Boundary value problems

Published online by Cambridge University Press:  26 February 2010

N. Chernyavskaya  and
L. Shuster
N. Chernyavskaya
Affiliation:
Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva, Israel.
L. Shuster
Affiliation:
Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan, 52900, Israel.
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Abstract

Consider the equation

where , . The inversion problem for (1) is called regular in Lp if, uniformly in p∈[1, ∞] for any f(x)∈ Lp(R), equation (1) has a unique solution y(x)∈ Lp(R) of the form

with . Here G(x, t) is the Green function corresponding to (1) and c is an absolute constant. For a given s∈[l, ∞], necessary and sufficient conditions are obtained for assertions (2) and (3) to hold simultaneously:

(2) the inversion problem for (1) is regular in Lp;

(3) for any f(x)∈LS(R).

MSC classification

Secondary: 34B40: Boundary value problems on infinite intervals
Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999 , pp. 453 - 470
Copyright
Copyright © University College London 1999

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References

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