Abel-like differential equations with a unique limit cycle Original Research Article

For the family of scalar Abel-like equations x′=A(t)xn+bB(t)xmx′=A(t)xn+bB(t)xm, where View the MathML sourceA(t)=∑l=1kalsinil(t)cosjl(t), B(t)=sinib(t)cosib(t)B(t)=sinib(t)cosib(t), al,b∈Ral,b∈R, n,m,k,il,jl,ib,jb∈Z+n,m,k,il,jl,ib,jb∈Z+, n,m≥2n,m≥2, and k≥1k≥1, we characterize the existence of non-trivial limit cycles (periodic solutions that are isolated in the set of periodic solutions different from the trivial x(t)≡0x(t)≡0) in terms of n,m,k,il,jl,ib,jbn,m,k,il,jl,ib,jb.