LAUSR

AbstractWe consider the solvable intervals of three positive parameters λi$\lambda _{i}$ (i=1,2,3$i=1,2,3$) in which the second-order impulsive boundary value problem {−x″=a(t)xy+λ1g(t)f(x),01$\alpha>1$, then for λi∈[λi∗,+∞)$\lambda_{i}\in[\lambda _{i}^{*},+\infty)$ (i=1,3$i=1,3$) and λ2∈[λ∗,λ∗]$\lambda_{2}\in[\lambda_{*}, \lambda^{*} ]$, the above boundary value problem admits at least two positive solutions; (ii) if 0<α<1$0<\alpha<1$, then for λi∈(0,λi∗∗]$\lambda_{i}\in(0,\lambda_{i}^{**}]$ (i=1,2,3$i=1,2,3$), the above boundary value problem admits at least two positive solutions.