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 ) $u_{lambda}(t)$ of the problem is strongly increasing and depends continuously on the parameter λ.
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机译：应用特征值理论和α凹算子理论，我们建立了一些新的充分条件，以保证二阶脉冲微分方程参数正解的存在性和连续性。此外，还给出了正解的两个不存在的结果。特别地，我们证明了问题的唯一解uλ（t）$ u _ { lambda}（t）$大大增加，并且连续取决于参数λ。
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