Nonlocal Sturm-Liouville problems with integral terms in the boundary conditions

Abstract

We consider a new type Sturm-Liouville problems whose main feature is the nature of boundary conditions. Namely, we study the nonhomo-geneous Sturm-Liouville equation (Formula Presented.) on two disjoint intervals [?1, 0) and (0, 1], subject to the nonlocal boundary-transmission conditions (Formula Presented.) where ? 1 := [-1, 0), ? 2 := (0, 1] and x kj ? (-1, 0) ? (0, 1) are internal points. By using our own approaches we establish such important properties as Fred-holmness, coercive solvability and isomorphism with respect to the spectral parameter ?. ©2017 Texas State University.