Fixed point theorem on functional intervals for sum of two operators and application in ODEs

In this paper, we present a generalization of the functional expansion-compression fixed point theorem developed by Avery et al. in [5] to the case of a k-set contraction perturbed by an operator T, where I -T is Lipschitz invertible. The arguments are based upon recent fixed point index theory in cones of Banach spaces. Next, we apply the obtained result to discuss the existence of a nontrivial positive solution to a nonautonomous second order boundary value problem.