A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions

摘要

This paper concerns the monotone approximations of solutions of boundary value problems such as−u″+f(t,u,u′)=0,u′(0)=u′(1)=0.We consider linear iterative scheme in case f is Lipschitz in u′ and satisfies a one-sided Lipschitz condition in u. The initial approximations are lower and upper solutions which can be ordered one way (α⩽β) or the other (α⩾β). We also consider the periodic and the Dirichlet problems.