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【期刊论文】Controllability of impulsive neutral functional differential inclusions with infinite delay
刘斌, Bing Liu
B. Liu/Nonlinear Analysis 60(2005)1533-1552,-0001,():
-1年11月30日
The paper is concerned with the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in a Banach space. Sufficient conditions for controllability are obtained by using a fixed point theorem for condensing maps due to Martelli. As an application, we also consider an impulsive neutral partial functional differential equation.
Controllability, Mild solution, Convex multivalued map, Impulsive neutral functional differential inclusions, Infinite delay
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【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
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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【期刊论文】Existence and Uniqueness of Solutions to First-Order Multipoint Boundary Value Problems
刘斌, BING LIU
Applied Mathematics Letters 17(2004)130-1316,-0001,():
-1年11月30日
this paper, we give existence and uniqueness results for solutions of multipoint boundary value problems of the form x'=ƒ(t,x(t))+e(t), t∈(0,1), m∑j=1/Ajx (ηj)=0, where ƒ: [0, 1] x Rn→Rn is s Carathdodory function, Ajs (j=1, 2,……,m) are constant square matrices of order n1, 0<η1<η2<…<ηm-1<ηm<1, and e(t) ∈L1([0, 1], Rn). The existence of solutions is proven by the coincidence degree theory. As an application, we also give one example to demonstrate our results.
First-order system, Existence and uniqueness of solution, Multipoint boundary value problems, Fredholm operator, Coincidence degree.,
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30浏览
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刘斌, Huaiqiang Yu and Bin Liu
J. Math. Anal. Appl. 395 (2012) 654–672,-0001,():
-1年11月30日
We study the boundary control problems for stochastic parabolic equations with Neumann boundary conditions. Imposing super-parabolic conditions, we establish the existence and uniqueness of the solution of state and adjoint equations with non-homogeneous boundary conditions by the Galerkin approximations method. We also find that, in this case, the adjoint equation (BSPDE) has two boundary conditions (one is non-homogeneous, the other is homogeneous). By these results we derive necessary optimality conditions for the control systems under convex state constraints by the convex perturbation method.
Stochastic partial differential equations, Boundary control, Necessary conditions
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【期刊论文】Controllability of Nonlinear Neutral Evolution Integrodifferential Systems with Infinite Delay
刘斌, B. Liu
JOTA: VOL. 122, NO.1, JULY 2004, 99-109,-0001,():
-1年11月30日
Sufficient conditions are derived for the controllability of nonlinear neutral evolution integrodifferential systems with infinite delay in a Banach space. The results are obtained by using the resolvent operators and the Schaefer fixed-point theorem. An example is given to illustrate the results.
Controllability, mild solutions, resolvent operators, neutral evolution integrodifferential systems, infinite delays.,
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