Ö. Uğur and M. Akhmet, Boundary Value Problems for Higher Order Linear Impulsive Differential Equations, Journal of Mathematical Analysis and Applications, 319(1), pp. 139-156, (July 2006).
In this paper higher order linear impulsive differential equations with fixed moments of impulses subject to linear boundary conditions are studied. Green's formula is defined for piecewise differentiable functions. Properties of Green's functions for higher order impulsive boundary value problems are introduced. An appropriate example of the Green's function for a boundary value problem is provided. Furthermore, eigenvalue problems and basic properties of eigensolutions are considered.
Keywords: impulsive differential equations, boundary value problems, eigenvalue problems, Green's function