Abstract
We study the limit cycles of the fifth-order differential equation x⋅⋅⋅⋅⋅−ex⃜−dx⃛−cx¨−bx˙−ax=εFx,x˙,x¨,x⋯,x⃜ with a=λμδ,b=−λμ+λδ+μδ,c=λ+μ+δ+λμδ,d=−1+λμ+λδ+μδ,e=λ+μ+δ, where ε is a small enough real parameter, λ,μ, and δ are real parameters, and F∈C2 is a nonlinear function. Using the averaging theory of first order, we provide sufficient conditions for the existence of limit cycles of this equation.