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

Abstract

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