Periodic solutions and their stability of some higher-order positively homogenous differential equations

In the present paper we study periodic solutions and their stability of the m-order differential equations of the form x(m)+fn(x)=μh(t),where the integers m, n ≥ 2, fn(x)=δxn or δ|x|n with δ=±1,h(t) is a continuous T-periodic function of non-zero average, and μ is a positive small parameter. By using the averaging theory, we will give the existence of T-periodic solutions. Moreover, the instability and the linear stability of these periodic solutions will be obtained.