Applications of Conley index theory on difference equations with non-resonance (Q2005971)

The main result of the paper provides the existence of nontrivial \(N\)-periodic solutions of the difference equation \(\Delta^2x_{n-1}+\nabla F_n(x_n)=0\), where \(F_n=F_{n+N}\), \(F_n\) is of class \(C^2\), the gradient \(\nabla F_n\) is asymptotically linear both at \(0\) and at \(\infty\), and the matrices corresponding to the asymptotic linearity satisfy additional conditions related to non-resonance and to the values of Morse indices and nullity. The proofs are based on Conley index theory.