  In this paper, we investigate the equilibria and their stability in an
asymmetric duopoly model of Kopel by using several tools based on symbolic
computations. We explore the possible positions of the equilibria in Kopel's
model. We discuss the possibility of the existence of multiple positive
equilibria and establish a necessary and sufficient condition for a given
number of equilibria to exist. Furthermore, if the two duopolists adopt the
best response reactions or homogeneous adaptive expectations, we establish
rigorous conditions for the existence of distinct numbers of positive
equilibria for the first time.
