A NEW SIMPLE PROOF FOR THE LUM-CHUA'S CONJECTURE

In this paper, using the theory of inverse integrating factor, we provide a new simple proof for the Lum-Chua's conjecture, which says that a continuous planar piecewise linear differential system with two zones separated by a straight line has at most one limit cycle. In addition, we prove that if this limit cycle exists, then it is hyperbolic and its stability is characterized in terms of the parameters. To the best of our knowledge, the hyperbolicity of the limit cycle has not been pointed out before.