Difference Equations Associated with Boundary Value Problems for Second Order Nonlinear Ordinary Differential Equations

摘要

The continuous problem and its variations have been the subject of extensive study resulting in several existence theories which are nonconstructive but which are very general and apply to problems having multiple solutions. In the paper the author studies the discrete problem and its relationship to the continuous problem and obtains versions of these existence theories which are as explicitly constructive as possible but which also retain much of the generality. The line of attack is to first obtain a priori bounds independent of h on solutions to the discrete problem and their first differences, and then use these bounds in conjunction with the Brouwer fixed point theorem to obtain existence of solutions to the discrete problem. (Author)