In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also ex...In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also extended and improved in this paper.展开更多
In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence o...In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence of periodic solutions of a type of neutral functional equation system are obtained,and at the same time, we present a method with formula shows how to find the periodicsolutions.展开更多
The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms....The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms.When the control region is convex, a pointwise second-order necessary condition for stochastic singular optimal controls in the classical sense is established; while when the control region is allowed to be nonconvex, we obtain a pointwise second-order necessary condition for stochastic singular optimal controls in the sense of Pontryagin-type maximum principle. It is found that, quite different from the first-order necessary conditions,the correction part of the solution to the second-order adjoint equation appears in the pointwise second-order necessary conditions whenever the diffusion term depends on the control variable, even if the control region is convex.展开更多
文摘In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also extended and improved in this paper.
文摘In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence of periodic solutions of a type of neutral functional equation system are obtained,and at the same time, we present a method with formula shows how to find the periodicsolutions.
基金supported by the National Basic Research Program of China(973 Program)(Grant No.2011CB808002)National Natural Science Foundation of China(Grant Nos.11221101+4 种基金1123100711401404 and 11471231)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT1273)the Changjiang Scholars Program from the Chinese Education Ministrythe Spanish Science and Innovation Ministry(Grant No.MTM2011-29306)
文摘The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms.When the control region is convex, a pointwise second-order necessary condition for stochastic singular optimal controls in the classical sense is established; while when the control region is allowed to be nonconvex, we obtain a pointwise second-order necessary condition for stochastic singular optimal controls in the sense of Pontryagin-type maximum principle. It is found that, quite different from the first-order necessary conditions,the correction part of the solution to the second-order adjoint equation appears in the pointwise second-order necessary conditions whenever the diffusion term depends on the control variable, even if the control region is convex.
