Uniqueness of periodic solutions for certain second-order equations (Q1887417)

Subject of the paper is the class of planar differential systems \[ dx/dt= y,\quad dy/dt= -f(x)(A| y|^a+ B| y|^b)y- g(x). \] The authors impose a standard type of conditions on the continuous functions \(f\), \(g\) and some inequalities among the nonnegative constants \(A\), \(B\), \(a\), \(b\) to prove that the system has at most one limit cycle in a certain vertical strip. The proof is similar to many others in this field, using well established arguments such as the theory of rotated vector fields.