Ö. Uğur and M. Akhmet, The Sturm-Liouville Operator on the Space of Functions with Discontinuity Conditions, Computers & Mathematics with Applications, 51(6-7), pp. 889-896, (March-April 2006).
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.
Keywords: impulsive differential equation, boundary value problem, Sturm-Liouville problem, eigenvalue problem