An iterative method for a class of quasilinear boundary value problems

Let n ≥ 3 . In this paper, we consider the following general quasilinear boundary value problem of second order { u ″ ( t ) + n − 1 t u ′ ( t ) + f ( t , u ( t ) ) = 0 , a . e . t ∈ [ 0 , 1 ] , u ′ ( 0 ) = 0 , u ( 1 ) = 0 , where the nonlinear term f ( t , u ) is a strong Carathéodory function. By applying the monotonically iterative technique, we construct a sequence of successive approximations and prove that the sequence converges uniformly to the solution of the above problem under suitable assumptions.