On the number of limit cycles for a class of discontinuous quadratic differential systems

The present paper is devoted to the study of the maximum number of limit cycles bifurcated from the periodic orbits of the quadratic isochronous center x˙=−y+163x2−43y2,y˙=x+83xy by the averaging method of first order, when it is perturbed inside a class of discontinuous quadratic polynomial differential systems. The Chebyshev criterion is used to show that this maximum number is 5 and can be realizable. In some sense, the result and that in paper [6] also answer the questions left in the paper [9].