Unbounded solutions of differential equations of second order

摘要

In this paper, the existence of unbounded solutions for the following nonlinear asymmetric oscillator $${{x}ifmmode{'}else$'$fi}ifmmode{'}else$'$fi + f(x){x}ifmmode{'}else$'$fi + alpha x^{ + } - beta x^{ - } = h(t)$$ is discussed, where α, β are positive constants satisfying $$frac{1}{{{sqrt alpha }}} + frac{1}{{{sqrt beta }}} = frac{2}{omega }$$ for some ω ∈R + /Q, h(t) ∈L ∞ [0, 2π ] is 2π-periodic, x ±=max {±x, 0 }.