On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line

In this paper we study the maximum number $N$ of limit cycles that can exhibit a planar piecewise linear differential system formed by two pieces separated by a straight line. More precisely, we prove that this maximum number satisfies $2\leq N \leq 3$ if one of the two linear differential systems has its equilibrium point on the straight line of discontinuity.

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