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

作者：El Gebeily Mohamed^*; O'Regan Donal

来源：Nonlinear Analysis: Real World Applications , 2007, 8(1): 174-186.

DOI：10.1016/j.nonrwa.2005.06.008

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

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.

• 出版日期2007-2
• 单位中国石油大学（北京）