On completeness of weak eigenfunctions for multi-interval Sturm-Liouville equations with boundary-interface conditions

Abstract The goal of this study is to analyse the eigenvalues and weak eigenfunctions a new type multi-interval Sturm-Liouville problem (MISLP) which differs from standard problems (SLPs) in that Strum-Liouville equation defined on finite number non-intersecting subintervals boundary conditions are set not only at endpoints but also internal points interaction. For self-adjoint treatment considered MISLP, we introduced some linear operators such way SLPs can be interpreted as operator-pencil equation. First, concept solutions (eigenfunctions) for MISLPs with interface common ends subintervals. Then, found important properties corresponding eigenfunctions. In particular, proved spectrum discrete system forms Riesz basis appropriate Hilbert space.