Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4623809 | Journal of Mathematical Analysis and Applications | 2006 | 14 Pages |
Abstract
In this paper we discuss some existence results and the application of quasilinearization methods, developed so far for differential equations, to the solution of the abstract problem in a Hilbert space H. Under fairly general assumptions on , F and H, we show that this problem has a solution that can be obtained as the limit of a quadratically convergent nondecreasing sequence of approximate solutions. If the assumptions are strengthened, we show that the abstract problem has a solution which is quadratically bracketed between two monotone sequences of approximate solutions of certain related linear equations.
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