Abstract generalized quasiliniarization method for coincidences


An abstract unified theory of both monotone iterative and generalized quasilinearization methods is presented for operator equations of coincidence type in ordered Banach spaces. Applications are given for semilinear problems in \(C(\overline{\Omega};\mathbb{R}^k)\) and \(L^p(\Omega;\mathbb{R}^k)\).


Adriana Buica
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


generalized quasilinearization;  monotone iterative technique;  upper and lower solutions; quadratic convergence;  coincidence; ordered Banach space.

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A. Buica, R. Precup, Abstract generalized quasiliniarization method for coincidences, Nonlinear Stud., 9 (2002), 371-387.


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Nonlinear Studies

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MR 1940557, Zbl 1020.65031

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