The recent literature on uncertainty and capital accumulation has focused on the effects of ‘real options’ associated with irreversible investment (e.g. Dixit and Pindyck, 1994; Abel and Eberly, 1996). The focus has been primarily on short run mechanisms. For example it has been shown that, at a higher level of uncertainty, risk neutral firms are less likely to invest in response to a positive ...

In this paper, we show that there are solutions of degree r the equation Pell–Abel on some real hyperelliptic curve genus g if and only r>g. This result, which is known to experts, has consequences, seem be unknown experts. First, deduce existence a primitive k-differential an with unique zero order k(2g-2) for every (k,g)≠(2,2). Moreover, exists non Weierstrass point n modulo n>2g.

This article provides sufficient conditions for the existence of periodic solutions with nonconstant sign in a family of polynomial, non-autonomous, first-order differential equations that arise as a generalization of the Abel equation of the second kind.