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Nontrivial periodic solutions to delay difference equations via Morse theory. (English) Zbl 1412.39014

The authors study the problem of existence of nontrivial periodic solutions of the asymptotically linear delay difference equation \[ \Delta x(t) = -f(x(t-T)), \] where \(f(-x)=-f(x)\) is a continuous function from \(\mathbb{R}^n\) to \(\mathbb{R}^n\). The problem is mapped to a critical point problem in a Hilbert space, and the existence result is proved by using Morse theory.

MSC:

39A23 Periodic solutions of difference equations
39A06 Linear difference equations
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