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

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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
State	Published - 1 Mar 2010

Bibliographical note

Funding Information:
The research of M. El-Gebeily is supported by King Fahd University of Petroleum and Minerals, project # IP2009-39. The research of J.J. Nieto has been partially supported by Ministerio de Educacion y Ciencia and FEDER, project MTM2007-61724, and by Xunta de Galicia and FEDER, project PGIDIT06PXIB207023PR.

Keywords

Cauchy problem
Existence
Monotone operators
Nonlinear operators
Partially ordered spaces

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2009.10.024

Cite this

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title = "A monotone iterative technique for stationary and time dependent problems in Banach spaces",

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.",

keywords = "Cauchy problem, Existence, Monotone operators, Nonlinear operators, Partially ordered spaces",

author = "El-Gebeily, \{M. A.\} and Donal O'Regan and Nieto, \{J. J.\}",

note = "Funding Information: The research of M. El-Gebeily is supported by King Fahd University of Petroleum and Minerals, project \# IP2009-39. The research of J.J. Nieto has been partially supported by Ministerio de Educacion y Ciencia and FEDER, project MTM2007-61724, and by Xunta de Galicia and FEDER, project PGIDIT06PXIB207023PR.",

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doi = "10.1016/j.cam.2009.10.024",

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T1 - A monotone iterative technique for stationary and time dependent problems in Banach spaces

AU - El-Gebeily, M. A.

AU - O'Regan, Donal

AU - Nieto, J. J.

N1 - Funding Information: The research of M. El-Gebeily is supported by King Fahd University of Petroleum and Minerals, project # IP2009-39. The research of J.J. Nieto has been partially supported by Ministerio de Educacion y Ciencia and FEDER, project MTM2007-61724, and by Xunta de Galicia and FEDER, project PGIDIT06PXIB207023PR.

PY - 2010/3/1

Y1 - 2010/3/1

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

U2 - 10.1016/j.cam.2009.10.024

DO - 10.1016/j.cam.2009.10.024

M3 - Article

AN - SCOPUS:73249116341

SN - 0377-0427

VL - 233

SP - 2395

EP - 2404

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 9

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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