Bifurcation of limit cycles by perturbing piecewise smooth integrable non-Hamiltonian systems

This paper deals with bifurcation of limit cycles for piecewise smooth integrable non-Hamiltonian systems. We derive the first order Melnikov function, which plays an important role in the study of the number of limit cycles bifurcated from the periodic annulus of a center. As an application, we consider a class of cubic isochronous centers, which has a non-rational first integral. Using the first order Melnikov function, we obtain the sharp upper bound of the number of limit cycles which bifurcate from the periodic annulus of the center under piecewise smooth polynomial perturbations.