Abstract

Massera′s Theorem provides sufficient conditions for the existence of at most one limit cycle for a class of Liénard differential systems of the form $x\prime \; =\; y$, $y\prime =\; -f(x)y-x$. Here we provide a new approach to this theorem and we extend it to a new class of Liénard differential systems of the form $x\prime \; =\; y$, $y\prime =\; -f(x)y-g(x)$. Finally we apply this new result to prove the Lins, de Melo and Pugh conjecture for degree 4.