The quasilinearization method on an unbounded domain

Author:
Paul W. Eloe

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1481-1488

MSC (1991):
Primary 34B40, 34A45

DOI:
https://doi.org/10.1090/S0002-9939-02-06654-6

Published electronically:
September 20, 2002

MathSciNet review:
1949878

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Abstract | References | Similar Articles | Additional Information

Abstract: We apply a method of quasilinearization to a boundary value problem for an ordinary differential equation on an unbounded domain. A uniquely determined Green's function, which is integrable and of fixed sign, is employed. The hypotheses to apply the quasilinearization method imply uniqueness of solutions. The quasilinearization method generates a bilateral iteration scheme in which the iterates converge monotonically and quadratically to the unique solution.

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Additional Information

**Paul W. Eloe**

Affiliation:
Department of Mathematics, University of Dayton, Dayton, Ohio 45469-2316

Email:
Paul.Eloe@notes.udayton.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06654-6

Keywords:
Quasilinearization,
quadratic convergence,
upper and lower solutions,
singular boundary value problems

Received by editor(s):
August 10, 2001

Received by editor(s) in revised form:
December 11, 2001

Published electronically:
September 20, 2002

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2002
American Mathematical Society