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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
Published electronically: September 20, 2002
MathSciNet review: 1949878
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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

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

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