Response Solutions for Degenerate Reversible Harmonic Oscillators with Zero-average Perturbation

In this paper,we consider a class of normally degenerate quasi-periodically forced reversible systems,obtained as perturbations of a set of harmonic oscillators,■ where 0≠λ∈R,l>1 is an integer and the corresponding involution G is(-θ,x,-y)→(θ,x,y).The existence of response solutions of the above reversible systems has already been proved in 22]if f₂(ωt,0,0)] satisfies some non-zero average conditions(See the condition(H) in 22]),here ·]denotes the average of a continuous functi...