Solutions of Two-point BVP in Banach Spaces

The two point boundary value problem(BVP) with general boundary value conditions in Banach spaces is considered. Using the Green function of the two point BVP on R 1 and beginning at its upper solution v 0 and then at its lower solution u 0, monotone iterative sequences are constructed in ordered interval [u 0, v 0] and it is proved that the sequences converge to their maximal and minimal solutions, respectively. Moreover, it is shown that the sequence, as above, converges to the unique solution of the BVP for any initial value on the ordered interval [u 0, v 0]. Also, the error estimate of the solution's converging sequence is given.