THE NUMBER OF INTEGRABLE-SQUARE SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS

摘要

where the p(x) are in general complex-valued functions satisfying various continuity conditions. Suppose further that M is formally self-adjoint. If the p.(x) are real-valued, then it is well known that, if S denotes the maximum number of linearly independent L2 (0,°°) solutions of the equation My , then S is independent of if im 0 . Even if the p (x) are complex-valued, S is constant for im > 0 and for im < 0, although it has not hitherto been established whether the two constant values need be the same. This note gives an example to show that they need not be.