Positive solutions for a class of non-autonomous second order difference equations via a new functional fixed point theorem

Abstract

. In this paper, by using recent results on fixed point index, we develop a new fixed point theorem of functional type for the sum of two operators T + S where I − T is Lipschitz invertible and S a k -set contraction. This fixed point theorem is then used to establish a new result on the existence of positive solutions to a non-autonomous second order difference equation.