Upper and lower solutions and quasilinearization for a class of second order singular nonlinear differential equations with nonlinear boundary conditions

Donal O'Regan

doi:10.1016/j.nonrwa.2006.02.001

Upper and lower solutions and quasilinearization for a class of second order singular nonlinear differential equations with nonlinear boundary conditions

Donal O'Regan

Mathematics

King Fahd University of Petroleum and Minerals

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

13 Citations (Scopus)

Abstract

We consider the differential equation -(1 w)(pu)=f((.), u), where f is a nonlinear function, 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. (c) 2006 Elsevier Ltd. All rights reserved.

Original language	English (Ireland)
Pages (from-to)	636-645
Number of pages	10
Journal	Nonlinear Analysis-Real World Applications
Volume	8
Issue number	2
DOIs	https://doi.org/10.1016/j.nonrwa.2006.02.001
Publication status	Published - 1 Apr 2007

Keywords

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

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

Authors
El-Gebeily, M,O'Regan, D

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10.1016/j.nonrwa.2006.02.001

Cite this

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abstract = "We consider the differential equation -(1 w)(pu)=f((.), u), where f is a nonlinear function, 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. (c) 2006 Elsevier Ltd. All rights reserved.",

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N2 - We consider the differential equation -(1 w)(pu)=f((.), u), where f is a nonlinear function, 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. (c) 2006 Elsevier Ltd. All rights reserved.

AB - We consider the differential equation -(1 w)(pu)=f((.), u), where f is a nonlinear function, 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. (c) 2006 Elsevier Ltd. All rights reserved.

KW - Nonlinear boundary conditions

KW - Nonlinear ordinary differential equations

KW - Quasilinearization method

KW - Upper and lower solutions

UR - https://www.scopus.com/pages/publications/33845580079

U2 - 10.1016/j.nonrwa.2006.02.001

DO - 10.1016/j.nonrwa.2006.02.001

M3 - Article

VL - 8

SP - 636

EP - 645

JO - Nonlinear Analysis-Real World Applications

JF - Nonlinear Analysis-Real World Applications

IS - 2

ER -

Upper and lower solutions and quasilinearization for a class of second order singular nonlinear differential equations with nonlinear boundary conditions

Abstract

Keywords

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

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