Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer s fixed point theorem and the counter pro...Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer s fixed point theorem and the counter proof method,and some sufficient conditions for the global asymptotic stability of the equilibrium point are obtained through the combination of a suitable Lyapunov function and an algebraic inequality technique.展开更多
This paper studies the existence, uniqueness, and stability of solutions for stochastic impulsive systems. By employing Lyapunov-like functions, some sufficient conditions of the global existence, uniqueness, and stab...This paper studies the existence, uniqueness, and stability of solutions for stochastic impulsive systems. By employing Lyapunov-like functions, some sufficient conditions of the global existence, uniqueness, and stability of solutions for stochastic impulsive systems are established. Furthermore, the results are specialized to the case of linear stochastic impulsive systems. Finally, some examples are given to illustrate the applications of our theory.展开更多
The global stability of Lipschitz continuous solutions with discontinuous initial data for the relativistic Euler equations is established in a broad class of entropy solutions in L∞ containing vacuum states. As a co...The global stability of Lipschitz continuous solutions with discontinuous initial data for the relativistic Euler equations is established in a broad class of entropy solutions in L∞ containing vacuum states. As a corollary, the uniqueness of Lipschitz solutions with discontinuous initial data is obtained in the broad class of entropy solutions in L∞.展开更多
Most known results on existence, uniqueness and stability for solutions of the polynomial-like iterative equation ∑ni=1λifi（x） = F（x） were obtained in the case of λ1 ≠0. In this paper, we construct Co decreasi...Most known results on existence, uniqueness and stability for solutions of the polynomial-like iterative equation ∑ni=1λifi（x） = F（x） were obtained in the case of λ1 ≠0. In this paper, we construct Co decreasing solutions of the iterative equation in the case that A1 can vanish to answer the Leading Coeffi- cient Problem. Moreover, we also give the necessary and sufficiently condition for uniqueness of solutions.展开更多
The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in s...The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in some cases asymptotic behaviour.展开更多
基金Research supported by the National Natural Science Foundation of China(12271220)postgraduate research and practice innovation program of Jiangsu Province(KYCX24-3010)。
文摘Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer s fixed point theorem and the counter proof method,and some sufficient conditions for the global asymptotic stability of the equilibrium point are obtained through the combination of a suitable Lyapunov function and an algebraic inequality technique.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 60274007, and the Post Doctoral Foundation of China and the Excellent Young Program of the Education Department of Hunan Province under Grant No. 04B068, and the NSERC-Canada.
文摘This paper studies the existence, uniqueness, and stability of solutions for stochastic impulsive systems. By employing Lyapunov-like functions, some sufficient conditions of the global existence, uniqueness, and stability of solutions for stochastic impulsive systems are established. Furthermore, the results are specialized to the case of linear stochastic impulsive systems. Finally, some examples are given to illustrate the applications of our theory.
基金Project supported by the National Natural Science Foundation of China (No.10101011) the Natural Science Foundation of Shanghai (No.04ZR14090).
文摘The global stability of Lipschitz continuous solutions with discontinuous initial data for the relativistic Euler equations is established in a broad class of entropy solutions in L∞ containing vacuum states. As a corollary, the uniqueness of Lipschitz solutions with discontinuous initial data is obtained in the broad class of entropy solutions in L∞.
基金supported by National Natural Science Foundation of China(Grant No.11201184)the Natural Science Foundation of Chongqing Normal University(Grant No. 12XLB019)
文摘Most known results on existence, uniqueness and stability for solutions of the polynomial-like iterative equation ∑ni=1λifi（x） = F（x） were obtained in the case of λ1 ≠0. In this paper, we construct Co decreasing solutions of the iterative equation in the case that A1 can vanish to answer the Leading Coeffi- cient Problem. Moreover, we also give the necessary and sufficiently condition for uniqueness of solutions.
基金Project supported by the Swiss National Science Foundation under the contract#20-67618.02.
文摘The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in some cases asymptotic behaviour.
