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in which the German capital letters designate matrices of the order two and the solution u(x) is a vector, that is, a matrix of two rows and one column. In either form the parameter X is to be taken as complex and unbounded, while the variable x is to be taken as real and on the finite interval (a, 6). On this interval the coefficients pik{x), or the elements of the matrices $*(*), are assumed to be differentiable, and such that the functions r{x) which, in the case of the system (1.1), satisfy the equation

A theory for ordinary differential boundary problems of the second order and of the highly irregular type