Fernanda Becatti, Jaume Llibre
Abstract There are many papers dedicated to study the limit cycles of either continuous, or discontinuous piecewise linear differential systems separated by one straight line in the plane $$\mathbb {R}^2$$ R 2 . Here by first time we shall study the limit cycles of piecewise linear differential systems separated by one straight line in the plane $$\mathbb {R}^2$$ R 2 that are continuous in one component of differential system and discontinuous in the other.