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2013年04月06日

【期刊论文】Lp-solutions of Fokker–Planck equations

刘斌， Jinlong Wei and Bin Liu

Nonlinear Analysis 85 (2013) 110–124，-0001，（）：

-1年11月30日

We obtain the existence and uniqueness of Lp-solutions (1 ≤ p ≤ ∞) for Fokker–Planck equations with irregular and degenerate coefficients. Moreover, as an application, we also derive the existence and uniqueness of L1-solutions for the Fokker–Planck–Boltzmann equation.

Transport equation， Lp-solution， Existence ， Fokker–Planck equation，

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2013年04月06日

【期刊论文】The existence and uniqueness of the solution for nonlinear Kolmogorov equations

刘斌， Jianjun Zhou and Bin Liu

J. Differential Equations 253 (2012) 2873–2915，-0001，（）：

-1年11月30日

摘要

By means of backward stochastic differential equations, the existence and uniqueness of the mild solution are obtained for the nonlinear Kolmogorov equations associated with stochastic delay evolution equations. Applications to optimal control are also given.

Kolmogorov equations， Stochastic delay evolution equations， Backward stochastic differential equations

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2013年04月06日

【期刊论文】Local existence-uniqueness and continuation of solutions for delay stochastic evolution equations

刘斌， Hanwen Ning and Bin Liu

Applicable Analysis, Vol. 88, No. 4, April 2009, 563–577，-0001，（）：

-1年11月30日

摘要

In this article, we consider dynamic behaviours of a class of non-linear delay stochastic evolution equations. Local existence and uniqueness of the solutions are obtained with the aid of proper iterative scheme and moment estimations. We also propose a continuation result and our results generalize the known results.

stochastic evolution equations， local existence， uniqueness，

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2013年04月06日

【期刊论文】Existence Results for Impulsive Neutral Stochastic Evolution Inclusions in Hilbert Space

刘斌， Hanwen Ning and Bin Liu

Acta Mathematica Sinica, 2011, 27(7), 1405–1418，-0001，（）：

-1年11月30日

摘要

This paper is concerned with the existence of mild solutions of a class of impulsive neutral stochastic evolution inclusions in Hilbert space in the case where the right hand side is convex or nonconvex-valued. The results are obtained by using two fixed point theorems for multivalued mappings and evolution system theory.

Impulsive,， mild solutions,， stochastic evolution inclusions,， convex,， nonconvex

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2013年04月06日

【期刊论文】A maximum principle for optimal control system with endpoint constraints

刘斌， Weifeng Wang and Bin Liu

Journal of Inequalities and Applications 2012, 2012，-0001，（）：

-1年11月30日

摘要

Pontryagin’s maximum principle for an optimal control system governed by an ordinary differential equation with endpoint constraints is proved under the assumption that the control domain has no linear structure. We also obtain the variational equation, adjoint equation and Hamilton system for our problem.

Pontryagin’s maximum principle， optimal control， Hamilton system，

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