Coercive Solvability of Two-Interval Sturm-Liouville Problems with Abstract Linear Operator

Abstract

In this paper we focus our attention on a new type nonhomogeneous Sturm-Liouville systems with abstract linear operator contained in the equation. A different approach is used here for investigation such important properties as topological isomorphism and coercive solvability. Moreover we prove that the corresponding resolvent operator is compact in a suitable Hilbert space.