By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.

We prove that there is a coincidence index for the inclusion F (x) ∈ Φ(x) when Φ is convex-valued and satisfies certain compactness assumptions on countable sets. For F we assume only that it provides a coincidence index for single-valued finite-dimensional maps (e.g. F is a Vietoris map). For the special case F = id, the obtained fixed point index is defined if Φ is countably condensing; the a...

Recently, Zhang and Song [Q. Zhang, Y. Song, Fixed point theory forgeneralized $varphi$-weak contractions,Appl. Math. Lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. In this paper, we prove a common fixed point theorem fora family of compatible maps. In fact, a new generalization of Zhangand Song's theorem is given.