Rate of Decay of Stable Periodic Solutions of Duffing Equations

In this paper, we consider the second-order equations of Duffing type. Bounds for the derivative of the restoring force are given that ensure the existence and uniqueness of a periodic solution. Furthermore, the stability of the unique periodic solution is analyzed; the sharp rate of exponential decay is determined for a solution that is near to the unique periodic solution.Comment: Key words: Periodic solution; Stability; Rate of deca

Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities

We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such that the equation has exactly three ordered T-periodic solutions. Moreover, when h is within these bounds, one of the three solutions is negative, while the other two are positive. The middle solution is asymptotically stable, and the remaining two are unstable.Comment: Keywords: Duffing equation; Periodic solution; Stabilit

Existence, uniqueness, and stability of periodic solutions of an equation of Duffing type

We consider a second-order equation of Duffing type. Bounds for the derivative of the restoring force are given which ensure the existence and uniqueness of a periodic solution. Furthermore, the unique periodic solution is asymptotically stable with sharp rate of exponential decay. In particular, for a restoring term independent of the variable $t$, a necessary and sufficient condition is obtained which guarantees the existence and uniqueness of a periodic solution that is stable.Comment: Key words and phrases: Periodic solution, topological degree, stabilit

Bank Discrimination in Transition Economies: Ideology, Information or Incentives?

We study bank discrimination against private firms in transition countries. Theoretically, we show that banks may discriminate for non-profit reasons, but this discrimination diminishes with a bank’s incentives and human capital. Employing matching bank-firm data from China, we empirically examine the extent, sources and consequences of discrimination. Our unique survey design allows us to disentangle sample truncation, omitted variable bias, and endogeneity issues. Our empirical findings confirm the theoretical predictions. We also find that as a result of discrimination, private firms resort to more expensive trade credits.http://deepblue.lib.umich.edu/bitstream/2027.42/39902/3/wp517.pd

INSIDER PRIVATIZATION WITH A TAIL: THE BUYOUT PRICE AND PERFORMANCE OF PRIVATIZED FIRMS IN RURAL CHINA

This paper studies insider privatization in transition economies. We show theoretically that the underperformance of insider-privatized firms could be due to the manager-cum-owner's lack of incentives after privatization. A screening theory predicts that a firm's postprivatization incentives increase with the firm's buyout price. The empirical results show that the buyout price decreases with the degree of information asymmetry and that a firm's postprivatization performance increases with the buyout price. We also find that the performance of premium-paying firms converges with that of private firms after privatization; in contrast, heavily discounted firms perform indistinguishably from government-owned firms.Political Economy,