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In this paper, we first establish the expression of positive Green’s function for a second-order impulsive differential equation with integral boundary conditions and a delayed argument. Furthermore, applying Legget-William’s fixed point theorem and Hölder’s inequality, we obtain the existence results of at least three positive solutions under three cases: p=1$p=1$, 1<p<+∞$1< p<+\infty$, and p=+∞$p=+\infty$. We discuss our problem with impulsive effects and a delayed argument. In this case, our results cover second-order boundary value problems without impulsive effects and delayed arguments and are compared with some recent results. Finally, we give an example to illustrate our main results.

boundary value problems

Positive Green’s function and triple positive solutions of a second-order impulsive differential equation with integral boundary conditions and a delayed argument