Extremal points for impulsive Lidstone boundary value problems

The first extremal point for a boundary value problem with impulse for an nth-order linear, ordinary differential equation is characterized by the existence of a nontrivial solution that lies in a cone. Cone theoretic arguments are applied to linear, monotone, compacts maps. To construct such maps, an impulse effect operator is constructed to complement the usual Greenʹs function approach. An application is made to a nonlinear problem.