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

We consider the differential equation -(1/w)(pu′)′+μu=Fu-(1/w)(pu′)′+μu=Fu, where F   is a nonlinear operator, with nonlinear boundary conditions. Under appropriate assumptions on p,w,Fp,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.