Electronic Journal of Qualitative Theory of Differential Equations (Nov 2010)
Generalized quasilinearization method for nonlinear boundary value problems with integral boundary conditions
Abstract
The quasilinearization method coupled with the method of upper and lower solutions is used for a class of nonlinear boundary value problems with integral boundary conditions. We obtain some less restrictive sufficient conditions under which corresponding monotone sequences converge uniformly and quadratically to the unique solution of the problem. An example is also included to illustrate the main result.