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

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

doi:10.1016/j.cam.2009.10.024

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

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

Mathematics

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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/10.1016/j.cam.2009.10.024
Publication status	Published - 1 Mar 2010

Keywords

Cauchy problem
Existence
Monotone operators
Nonlinear operators
Partially ordered spaces

Authors (Note for portal: view the doc link for the full list of authors)

Authors
El-Gebeily, MA;O'Regan, D;Nieto, JJ

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10.1016/j.cam.2009.10.024

Cite this

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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.",

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AU - El-Gebeily, M. A.

AU - O'Regan, Donal

AU - Nieto, J. J.

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N2 - 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.

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

UR - https://www.scopus.com/pages/publications/73249116341

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DO - 10.1016/j.cam.2009.10.024

M3 - Article

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VL - 233

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EP - 2404

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

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ER -

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

Abstract

Keywords

Authors (Note for portal: view the doc link for the full list of authors)

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