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 u λ ( t ) of the problem is strongly increasing and depends continuously on the parameter λ .