The aim of this talk is to present our some recent results of limit cycles in planar smooth and piecewise smooth Lienard differential systems, including existence, uniqueness, stability and hyperbolicity of limit cycles.
Moreover, using these results for the limit cycles together with other qualitative methods and techniques, we can obtain the exact number of limit cycles and further obtain the global dynamics and bifurcations in some biological and mechanical models.

Slides of the talk.