Nontrivial periodic solutions to delay difference equations via Morse theory
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.
scientific article; zbMATH DE number 7045454