Boundary value problems for nonoscillating operators with Cartesian sets of functionals (Q1874961)

The authors deal with a solvability condition for a boundary value problem which involves an \(n\)th-order differential operator \(L(y)= \sum_{k=0}^{n}p_{k}(x)y^{(n-k)}(x)\) together with \(n\) functionals \( l_{i}( y) =c_{i}\) with \(i=1,\dots,n.\) The boundary conditions \( l_{i}(y)\) are functionals over the space of continuous functions, and so should be understood as measures or distributions. A system of functionals is \(T\)-regular if \(l_{i}(p)=0\) \(\Rightarrow p=0\) for any polynomial \(p\) in a Chebyshev system of order \(n-1\). If the property remains true for a system of order \(m-1,\) where \(1\leq m\leq n\), then we say it is said to be Cartesian or \(D\)-regular. The authors provide a result on the solvability for operators in the nonoscillatory case with a \(D\)-regular system of functionals.