A monotone iterative technique for stationary and time dependent problems in Banach spaces

M.A. El-Gebeily; Donal O'Regan; J. J. Nieto

doi:10.13025/27332

A monotone iterative technique for stationary and time dependent problems in Banach spaces

M.A. El-Gebeily
, Donal O'Regan
, J. J. Nieto

Mathematics

King Fahd University of Petroleum and Minerals
Universidade de Santiago de Compostela

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

9 Citations (Scopus)

Abstract

An abstract monotone iterative method is developed for operators between partially ordered Banach spaces for the nonlinear problem L u = N u and the nonlinear time dependent problem u^′ = (L + N) u. Under appropriate assumptions on L and N we obtain maximal and minimal solutions as limits of monotone sequences of solutions of linear problems. The results are illustrated by means of concrete examples.

Original language	English
Pages (from-to)	2395-2404
Number of pages	10
Journal	Journal of Computational and Applied Mathematics
Volume	233
Issue number	9
DOIs	https://doi.org/10.13025/27332 https://doi.org/10.1016/j.cam.2009.10.024
Publication status	Published - 1 Mar 2010

Keywords

Cauchy problem
Existence
Monotone operators
Nonlinear operators
Partially ordered spaces

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10.13025/27332Licence: CC BY-NC-ND
10.1016/j.cam.2009.10.024

Cite this

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AB - An abstract monotone iterative method is developed for operators between partially ordered Banach spaces for the nonlinear problem L u = N u and the nonlinear time dependent problem u′ = (L + N) u. Under appropriate assumptions on L and N we obtain maximal and minimal solutions as limits of monotone sequences of solutions of linear problems. The results are illustrated by means of concrete examples.

KW - Cauchy problem

KW - Existence

KW - Monotone operators

KW - Nonlinear operators

KW - Partially ordered spaces

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A monotone iterative technique for stationary and time dependent problems in Banach spaces

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Keywords

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