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

We consider the differential equation -(1/w)(pu′)′=f(·,u)-(1/w)(pu′)′=f(·,u), where ff is a nonlinear function, 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.