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

Abstract

In the present paper we study periodic solutions and their stability of the m-order differential equations of the form x^(m) f_n(x) = h(t), where the integers m, n2, f_n(x)= x^n or $^ n with = 1, and h(t) is a continuous T-periodic function of non-zero average, and 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.