Existence and quasilinearization in Banach spaces

M. A. El-Gebeily; K. Al Shammari; Donal O'Regan

doi:10.1016/j.jmaa.2009.04.044

Existence and quasilinearization in Banach spaces

M. A. El-Gebeily, K. Al Shammari, Donal O'Regan

Mathematics

King Fahd University of Petroleum and Minerals

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

1 Citation (Scopus)

Abstract

We establish some existence results for the nonlinear problem A u = f in a reflexive Banach space V, without and with upper and lower solutions. We then consider the application of the quasilinearization method to the above mentioned problem. Under fairly general assumptions on the nonlinear operator A and the Banach space V, we show that this problem has a solution that can be obtained as the strong limit of two quadratically convergent monotone sequences of solutions of certain related linear equations.

Original language	English
Pages (from-to)	345-354
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	358
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2009.04.044
Publication status	Published - 15 Oct 2009

Keywords

Existence
Monotone operators
Nonlinear operators
Quasilinearization method

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

Authors
El-Gebeily, MA;Al Shammari, K;O'Regan, D

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10.1016/j.jmaa.2009.04.044

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AU - O'Regan, Donal

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N2 - We establish some existence results for the nonlinear problem A u = f in a reflexive Banach space V, without and with upper and lower solutions. We then consider the application of the quasilinearization method to the above mentioned problem. Under fairly general assumptions on the nonlinear operator A and the Banach space V, we show that this problem has a solution that can be obtained as the strong limit of two quadratically convergent monotone sequences of solutions of certain related linear equations.

AB - We establish some existence results for the nonlinear problem A u = f in a reflexive Banach space V, without and with upper and lower solutions. We then consider the application of the quasilinearization method to the above mentioned problem. Under fairly general assumptions on the nonlinear operator A and the Banach space V, we show that this problem has a solution that can be obtained as the strong limit of two quadratically convergent monotone sequences of solutions of certain related linear equations.

KW - Existence

KW - Monotone operators

KW - Nonlinear operators

KW - Quasilinearization method

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DO - 10.1016/j.jmaa.2009.04.044

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EP - 354

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Existence and quasilinearization in Banach spaces

Abstract

Keywords

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

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