Periodic solutions and limit cycles of mixed Lienard-type differential equations

Abstract

In the attractive research field of nonlinear differential equations, there are a few studies devoted to finding exact and explicit harmonic and isochronous periodic solutions and limit cycles. In this contribution, we present some classes of polynomial mixed Lienard-type differential equations that can generate many equations with exact solutions. These classes of equations constitute counterexamples of the classical existence theorems.

Keywords

• polynomial mixed lienard-type differential equations
• exact harmonic and isochronous periodic solutions
• exact algebraic limit cycles
• classical existence theorems