Resonance phenomena for asymmetric weakly nonlinear oscillator

We establish the coexistence of periodic solution and unbounded solution, the infinity of large-amplitude subharmonics for asymmetric weakly nonlinear oscillator x″ + a2x+— b2x- + h(x) = p(t) with h(±∞) = 0 and xh(x) → +∞(x → ∞ ), assuming that M(τ) has zeros which are all simple and M(τ) ≡ 0 respectively, where M(τ) is a function related to the piecewise linear equation x″ + a2x+— b2x-= p(t).