In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic dii^erential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem o...In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic dii^erential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem of a bounded continuous compact operator. Hence using the famous Hilbert-Schmidt spectrum theory, we can characterize the eigenvalues exactly.展开更多
In this paper, the difference equation for N-body type problem is established, which can be used to find the generalized solutions by computing the critical points numerically. And its validity is testified by an exam...In this paper, the difference equation for N-body type problem is established, which can be used to find the generalized solutions by computing the critical points numerically. And its validity is testified by an example from Newtonian Threebody problem with unequal masses.展开更多
The quasi-periodic pendulum type equations are considered. A sufficient and necessary condition of Lagrange stability for this kind of equations is obtained. The result obtained answers a problem proposed by Moser und...The quasi-periodic pendulum type equations are considered. A sufficient and necessary condition of Lagrange stability for this kind of equations is obtained. The result obtained answers a problem proposed by Moser under the quasi-periodic case.展开更多
基金The NSF (10601019 and J0630104) of ChinaChinese Postdoctoral Science Foundation and 985 Program of Jilin University.
文摘In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic dii^erential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem of a bounded continuous compact operator. Hence using the famous Hilbert-Schmidt spectrum theory, we can characterize the eigenvalues exactly.
基金Partially supported by the Talent Foundation(522-7901-01140418)of Northwest A&F University
文摘In this paper, the difference equation for N-body type problem is established, which can be used to find the generalized solutions by computing the critical points numerically. And its validity is testified by an example from Newtonian Threebody problem with unequal masses.
基金Partially supported by the NSF (10871203, 10601019) of Chinathe NCET (07-0386)of China
文摘The quasi-periodic pendulum type equations are considered. A sufficient and necessary condition of Lagrange stability for this kind of equations is obtained. The result obtained answers a problem proposed by Moser under the quasi-periodic case.
