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A formal framework for the analysis of Hopf bifurcations for a kind of delayed equation with -Laplacian and with a discrete time delay is presented, thus generalizing known results for the sunflower equation given by Somolinos in 1978. Also, under appropriate assumptions we prove the gradient-like behavior of the equation which, in turn, implies the non-existence of nonconstant periodic solutions. Our conditions improve previous results known in the literature for the standard case (x) =x.
Amster et al. (Sat,) studied this question.