Comparison, Existence, Uniqueness and Successive Approximations for Two-Point Boundary Value Problems

摘要

Bailey, Shampine and Waltman developed an existence theory for two-point boundary value problems of second order differential equations whose second members satisfy one-sided Lipschitz conditions. It is suggested that solutions should exist in a much more general situation. A comparison result is given and applied to uniqueness and existence of the Picard problem as well as to the convergence of successive approximation for this. (Atomindex citation 13:676222)