Nonautonomous Fold Bifurcations from Spectral Intervals of Higher Strict Multiplicity

Abstract

We provide two sufficient criteria for the bifurcation of bounded entire or homoclinic solutions to nonautonomous difference equations depending on a single real parameter. Our analysis is based on a nonhyperbolic solution, whose variational equation possesses exponential dichotomies on semiaxes ensuring that the corresponding critical spectral interval of the dichotomy spectrum has strict multiplicity $>1$. This extends earlier results on the fold bifurcation.