Existence results for second-order impulsive boundary value problems on time scales (Q1005272)

The authors consider the impulsive boundary value problem on time scales \[ \begin{aligned} &-y^{\Delta\Delta}(t)=f(t,y(t)) \,\, \text{a.e}\,\, t\in J:[0,1]\setminus\{t_1,\dots,t_p\},\\ &y(t_k^+)-y(t_k^-)=I_k(y(t_k^-)), \,\,\, k=1,\dots, p,\\ &y^{\Delta}(t_k^+)-y^{\Delta}(t_k^-)=\tilde I_k(y(t_k^-)), \quad k=1,\dots, p,\\ &y(0)=y(1)=0. \end{aligned} \] Some new results are obtained for the existence of one or three positive solutions, by using a fixed point theorem due to Krasnoselskii and Zabreiko, and the Leggett-Williams fixed point theorem, respectively.