A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions

Mohamed El-Gebeily; Donal O'Regan

doi:10.1016/j.nonrwa.2005.06.008

A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions

Mohamed El-Gebeily^*, Donal O'Regan

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

23 Scopus citations

Abstract

We consider the differential equation - (1 / w) (pu^′)^′ + μ u = Fu, where F is a nonlinear operator, with nonlinear boundary conditions. Under appropriate assumptions on p, w, F and the boundary conditions, the existence of solutions is established. If the problem has a lower solution and an upper solution, then we use a quasilinearization method to obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.

Original language	English
Pages (from-to)	174-186
Number of pages	13
Journal	Nonlinear Analysis: Real World Applications
Volume	8
Issue number	1
DOIs	https://doi.org/10.1016/j.nonrwa.2005.06.008
State	Published - Feb 2007

Bibliographical note

Funding Information:
Research for the first author has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.

Keywords

Nonlinear boundary conditions
Nonlinear ordinary differential equations
Quasilinearization method
Upper and lower solutions

ASJC Scopus subject areas

Analysis
General Engineering
General Economics, Econometrics and Finance
Computational Mathematics
Applied Mathematics

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10.1016/j.nonrwa.2005.06.008

Cite this

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title = "A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions",

abstract = "We consider the differential equation - (1 / w) (pu′)′ + μ u = Fu, where F is a nonlinear operator, with nonlinear boundary conditions. Under appropriate assumptions on p, w, F and the boundary conditions, the existence of solutions is established. If the problem has a lower solution and an upper solution, then we use a quasilinearization method to obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.",

keywords = "Nonlinear boundary conditions, Nonlinear ordinary differential equations, Quasilinearization method, Upper and lower solutions",

author = "Mohamed El-Gebeily and Donal O'Regan",

note = "Funding Information: Research for the first author has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274. ",

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T1 - A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions

AU - El-Gebeily, Mohamed

AU - O'Regan, Donal

N1 - Funding Information: Research for the first author has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.

PY - 2007/2

Y1 - 2007/2

N2 - We consider the differential equation - (1 / w) (pu′)′ + μ u = Fu, where F is a nonlinear operator, with nonlinear boundary conditions. Under appropriate assumptions on p, w, F and the boundary conditions, the existence of solutions is established. If the problem has a lower solution and an upper solution, then we use a quasilinearization method to obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.

AB - We consider the differential equation - (1 / w) (pu′)′ + μ u = Fu, where F is a nonlinear operator, with nonlinear boundary conditions. Under appropriate assumptions on p, w, F and the boundary conditions, the existence of solutions is established. If the problem has a lower solution and an upper solution, then we use a quasilinearization method to obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.

KW - Nonlinear boundary conditions

KW - Nonlinear ordinary differential equations

KW - Quasilinearization method

KW - Upper and lower solutions

UR - https://www.scopus.com/pages/publications/33750064584

U2 - 10.1016/j.nonrwa.2005.06.008

DO - 10.1016/j.nonrwa.2005.06.008

M3 - Article

AN - SCOPUS:33750064584

SN - 1468-1218

VL - 8

SP - 174

EP - 186

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 1

ER -

A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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