On the Number of Limit Cycles Bifurcating from a Quartic Reversible Center

This paper deals with the bifurcation of limit cycles from a quartic reversible and non-Hamiltonian system. By using the averaging theory and some mathematical technique on estimating the zeros of the function, we show that under small polynomial perturbation of degree 3n+1 , at most 3n-3 limit cycles bifurcate from the period annulus of the unperturbed system for n>3 , while at most 2 n limit cycles appear from the period annulus of the unperturbed system for n=1, 2, 3 . And the upper bound for the latter case is sharp.