The generalized quasilinearization method for second-order three-point boundary value problems

In this paper, we obtain the existence and uniqueness results for general second-order three-point boundary value problems by applying the method of upper and lower solutions together with Leray–Schauder degree, as well as obtaining monotone iteration schemes which converge quadratically to the uniq...

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Veröffentlicht in:	Nonlinear analysis 2008-05, Vol.68 (9), p.2779-2790
Hauptverfasser:	Pei, Minghe, Chang, Sung Kag
Format:	Artikel
Sprache:	eng
Schlagworte:	34B10 34B15 Exact sciences and technology Leray–Schauder degree Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Partial differential equations, boundary value problems Quadratic convergence Quasilinearization Sciences and techniques of general use Three-point boundary value problem Upper and lower solutions
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Zusammenfassung:	In this paper, we obtain the existence and uniqueness results for general second-order three-point boundary value problems by applying the method of upper and lower solutions together with Leray–Schauder degree, as well as obtaining monotone iteration schemes which converge quadratically to the unique solution of some specific second-order three-point boundary value problem by using the method of quasilinearization.
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2007.02.025