Existence and continuity of positive solutions on a parameter for second-order impulsive differential equations

Applying the eigenvalue theory and theory of α-concave operator, we establish some new sufficient conditions to guarantee the existence and continuity of positive solutions on a parameter for a second-order impulsive differential equation. Furthermore, two nonexistence results of positive solutions are also given. In particular, we prove that the unique solution uλ(t) of the problem is strongly increasing and depends continuously on the parameter λ.