On the uniqueness of the limit cycle for the Lienard equation, via comparison method for the energy level curves

The problem of uniqueness of limit cycles for the Lienard equation is investigated. Some sufficient conditions are presented which complement recent related results. The proofs are based on an energy level comparison method which guarantees that all the possible limit cycles intersect the lines x = α and x = β, being a < 0 < β the two nontrivial zeros of F(x). Some examples illustrate the range of applicability of the main results. ©Dynamic Publishers, Inc.