A unique limiting Green's function for a class of singular boundary value problems
The authors consider the linear \(n\)th order difference equation \((*)\) \(Pu(m) = 0\) together with some homogeneous two-point boundary conditions \(T(b,i)=0\) satisfied at the end points \(a,b\) (so, \(b-a\) is a positive integer). Assuming a right disfocality of \((*)\) on \(\{n \geq a\}\) as well as a sign condition on the coefficients of \(P\), the authors analyze the behavior of the Green functions for the \((b,i)\)-family of the boundary value problem and, particularly, obtain a unique limiting Green function as \(b \to \infty\). Its properties are also investigated.
scientific article; zbMATH DE number 641434