Infinitely many nonhomogeneous conditions

AbstractA general formula is given for the index of a linear manifold in Banach space. This is expressed in terms of the dimensions of linear manifolds. A fundamental result is established, called a Boundary-Form Formula, for linear manifolds. This is then used to study the existence of the solutions of boundary value problems for linear manifolds subject to finite or infinite nonhomogeneous boundary conditions. An application is made to study the deficiency index of a second-order ordinary differential operator by dividing an interval into infinite subintervals