Abstract
Inspired by Chang (1981) and Long (1990), we consider the existence of periodic solutions for second-order difference equations with asymptotically linear nonlinearity via Conley index theory. Moreover, when we study the following one-dimensional autonomous difference equations with form Δ2xn−1+f(xn)=0,n∈Z,xn∈R,we can derive at least three periodic solutions under suitable assumptions.
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