Abstract
In this paper, we consider the following second-order four-point boundary-value problems Δ2 u(k − 1)+f(k,u(k), Δu(k)) = 0,k ∈ {1,2,…,T}, u(0) = au(l 1), u(T+1) = bu(l 2). We give conditions on f to ensure the existence of at least three positive solutions of the given problem by applying a new fixed-point theorem of functional type in a cone. The emphasis is put on the nonlinear term involved with the first-order difference.
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