Solvability and coerciveness of multi-point Sturm–Liouville problems with abstract linear functionals

Abstract

Abstract In this paper, we consider a Sturm–Liouville problem with finite discontinuous points inside an interval and with abstract linear functionals in the boundary and transmission conditions. For such a problem, the properties such as isomorphism, Fredholmness, and coerciveness with respect to the spectral parameter are investigated.

Keywords

• Sturm–Liouville problems
• Transmission conditions
• Isomorphism
• Coerciveness
• Solvability