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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.

The quasilinearization method on an unbounded domain