The Sturm-Liouville operator on the space of functions with discontinuity conditions

Abstract

The Sturm-Liouville differential operators defined on the space of discontinuous functions, where the moments of discontinuity of the functions are interior points of the interval and the discontinuity conditions are linear have been studied. Auxiliary results concerning the Green's formula, boundary value, and eigenvalue problems for impulsive differential equations are emphasized.

Sturm-Liouville Problems with finitely many point $\delta-$interactions and eigen-parameter in boundary condition

“…We note that Sturm-Liouville problems with eigen-dependent boundary conditions and with transmission conditions have been investigated in [1], [3], [9], [13], [11], [12]. Furthermore Green's formula for impulsive differential equation has been studied in [16] and [17].…”