An iterative method for a class of quasilinear boundary value problems

摘要

Let n≥3. In this paper, we consider the following general quasilinear boundary value problem of second order {u″(t)+n−1tu′(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.