General boundary conditions for an ordinary linear differential system
Randal H. Cole · Transactions of the American Mathematical Society · 1964
b (1.2) 9 1h(A;)1J(a),) + 9J3(x,4)V(x,A)dx = 6(i), ~~~~~~~~a where the matrix 0J3(i)Q) is free from x and {ah} is a finite or infinite set of points on a fundamental interval [a, b]. Tamarkin [5] has considered the general case, but many of his results were obtained by limiting the discussion to the situation where 03(x,2)-?) or where no boundary points exist in the interior of the fundamental interval. In particular, he did not define the adjoint system for the general case. Wilder [9] and Cole [1] have treated the case of a finite set of points and no integral term. Langer [2] has developed the theory associated with a finite set of boundary points in a complex domain. Whyburn has made substantial contributions to the problem, including a summary [6; 8] of known results. He has also shown [7] that the condition (1.2) is, in a certain sense, equivalent to