On the method of complementary functions for linear and nonlinear two- point boundary value problems (Q1197423)

The paper presents a criterion for solving both linear and nonlinear two- point boundary value problems by the method of complementary functions contrary to an earlier claim by \textit{S. M. Roberts} and \textit{J. S. Shipman} [J. Optimization Theory Appl. 28, 77-88 (1979; Zbl 0416.34024)] that it was not possible. The analysis of the present paper can be generalized to multi-point boundary value problem and other boundary value problems. The authors claim that the two methods involve the same number of integrations as the method of particular solutions.