# Abstract generalized quasiliniarization method for coincidences

## Abstract

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 $$L^p(\Omega;\mathbb{R}^k)$$.

## Authors

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

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

## Keywords

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

## Paper coordinates

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

## PDF

##### Journal

Nonlinear Studies

##### Online ISSN

MR 1940557, Zbl 1020.65031

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