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

被引：19

作者：

El-Gebeily, Mohamed ^{[1
]}

O'Regan, Donal

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia

[2] Natl Univ Ireland Univ Coll Galway, Dept Math, Galway, Ireland

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2007年 / 8卷 / 01期

关键词：

nonlinear ordinary differential equations; nonlinear boundary conditions; upper and lower solutions; quasilinearization method;

D O I：

10.1016/j.nonrwa.2005.06.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the differential equation -(1/w)(pu')' + mu 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. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：174 / 186

页数：13

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